In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral...In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.展开更多
In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equa...In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.展开更多
In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm i...In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.展开更多
In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t）...In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t））dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as （x,λ） → （x0, λ0） in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]展开更多
Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, so...Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.展开更多
Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of ...We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition.Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.展开更多
The existence of periodic solution to nonlinear integral equations with infinite delay is studied in this paper. We prove that the g- uniform bounded and g- uniform ultimate bounded solutions implies the existence of ...The existence of periodic solution to nonlinear integral equations with infinite delay is studied in this paper. We prove that the g- uniform bounded and g- uniform ultimate bounded solutions implies the existence of periodic solutions using Schauder-Tychonov’s fixed point theorem in the phase space (Cg,|·|g).展开更多
In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.
In this paper,a new integral inequality is established by an elementary inequality and a generalization of this new integral inequality,and its application is presented.
In this paper, by applying Avery-Henderson fixed point theorem in a cone, we establish some new existence results of two positive periodic solutions for a type of nonlinear integral equations with variant delay.
In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes...In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes.Therefore,it is significant to enhance the steering stability of tracked vehicle with hydrostatic drive to meet the need of future battlefield.In this paper,a sliding mode control algorithm is proposed and applied to achieve desired yaw rates.The speed controller and the yaw rate controller are designed through the kinematics and dynamics analysis.In addition,the nonlinear derivative and integral sliding mode control algorithm is designed,which is supposed to efficiently reduce the integration saturation and the disturbances from the unsmooth road surfaces through a conditional integrator approach.Moreover,it improves the response speed of the system and reduces the chattering by the derivative controller.The hydrostatic tracked vehicle module is modeled with a multi-body dynamic software RecurDyn and the steering control strategy module is modeled by MATLAB/Simulink.The co-simulation results of the whole model show that the control strategy can improve the vehicle steering response speed and also ensure a smooth control output with small chattering and strong robustness.展开更多
The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was c...The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.展开更多
This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterization...This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.展开更多
This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorit...This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method.展开更多
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison res...In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.展开更多
In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for ...In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.展开更多
In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a sy...In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.展开更多
In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of...In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method.展开更多
A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced ...A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.展开更多
基金Supported by the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.14ZB0364)
文摘In this paper, we consider a general nonlinear integral operator Hαi, βi （ f1,..., fn ; g1,..., gn）（z）. Some results including coefficient problems, univalency condition and radius of convexity for this integral operator are given. Furthermore, we discuss the mapping properties between Hαi,βi （f1 , fn, ; g1,..., gn）（z） and subclasses of analytic functions with bounded boundary rotation. The same subjects for some corresponding classes are shown upon specializing the parameters in our main results.
文摘In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.
文摘In this paper,the approximate solutions for two different type of two-dimensional nonlinear integral equations:two-dimensional nonlinear Volterra-Fredholm integral equations and the nonlinear mixed Volterra-Fredholm integral equations are obtained using the Laguerre wavelet method.To do this,these two-dimensional nonlinear integral equations are transformed into a system of nonlinear algebraic equations in matrix form.By solving these systems,unknown coefficients are obtained.Also,some theorems are proved for convergence analysis.Some numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the proposed method.
文摘In the present paper we state some approximation theorems concerning point- wise convergence and its rate for a class of non-convolution type nonlinear integral opera- tors of the form：Tλ（f;x）=B∫AKλ（t,x,f（t））dr,x∈〈a,b〉λλA.In particular, we obtain the pointwise convergence and its rate at some characteristic points x0 off as （x,λ） → （x0, λ0） in LI 〈A,B 〉, where 〈 a,b 〉 and 〈A,B 〉 are is an arbitrary intervals in R, A is a non-empty set of indices with a topology and X0 an accumulation point of A in this topology. The results of the present paper generalize several ones obtained previously in the papers [191-[23]
基金The project is supported in part by the NSF of Guangdong Province (Grnat No. 940651) the SF of Key Discipline of the State Council Office of Overseas Chinese Affairs of China (Grant No.93-93-6)
文摘Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
基金Supported in part by the Natural Science Foundation of China under grants 11761010 and 61863001.
文摘We propose a multiscale projection method for the numerical solution of the irtatively regularized Gauss-Newton method of nonlinear integral equations.An a posteriori rule is suggested to choose the stopping index of iteration and the rates of convergence are also derived under the Lipschitz condition.Numerical results are presented to demonstrate the efficiency and accuracy of the proposed method.
基金supported by the National Natural Sciences Foundations of China (10771107)
文摘The existence of periodic solution to nonlinear integral equations with infinite delay is studied in this paper. We prove that the g- uniform bounded and g- uniform ultimate bounded solutions implies the existence of periodic solutions using Schauder-Tychonov’s fixed point theorem in the phase space (Cg,|·|g).
基金supported by the National Natural Science Foundation of China(No.60974025)
文摘In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.
基金supported by the National Natural Science Foundation of China(No.60674020)
文摘In this paper,a new integral inequality is established by an elementary inequality and a generalization of this new integral inequality,and its application is presented.
文摘In this paper, by applying Avery-Henderson fixed point theorem in a cone, we establish some new existence results of two positive periodic solutions for a type of nonlinear integral equations with variant delay.
基金Supported by the National Natural Science Foundation of China(51475044)。
文摘In the steering process of tracked vehicle with hydrostatic drive,the motion and resistance states of the vehicle are always of uncertain and nonlinear characteristics,and these states may undergoe large-scale changes.Therefore,it is significant to enhance the steering stability of tracked vehicle with hydrostatic drive to meet the need of future battlefield.In this paper,a sliding mode control algorithm is proposed and applied to achieve desired yaw rates.The speed controller and the yaw rate controller are designed through the kinematics and dynamics analysis.In addition,the nonlinear derivative and integral sliding mode control algorithm is designed,which is supposed to efficiently reduce the integration saturation and the disturbances from the unsmooth road surfaces through a conditional integrator approach.Moreover,it improves the response speed of the system and reduces the chattering by the derivative controller.The hydrostatic tracked vehicle module is modeled with a multi-body dynamic software RecurDyn and the steering control strategy module is modeled by MATLAB/Simulink.The co-simulation results of the whole model show that the control strategy can improve the vehicle steering response speed and also ensure a smooth control output with small chattering and strong robustness.
文摘The article is considering the third kind of nonlinear Volterra-Stieltjes integral equations with the solution by Lavrentyev regularizing operator. A uniqueness theorem was proved, and a regularization parameter was chosen. This can be used in further development of the theory of the integral equations in non-standard problems, classes in the numerical solution of third kind Volterra-Stieltjes integral equations, and when solving specific problems that lead to equations of the third kind.
基金The work of the author has been supported by the Deutache Forschungsgemeinschaft(DFG) under Grant Ho 1846/1-1
文摘This paper studies several problems , which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1] are chosen as a starting point for characterizations of functions in Besom spaces B(?)(0,1) with 0<σ<∞ and (1+σ)-1<γ<∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
文摘This paper discusses the numerical solutions for the nonlinear Fredholm integral equations of thesecond kind. On the basis of the Galerkin method, the author establishes a Galerkin algorithm, a Wavelet-Galerkinalgorithm and their corresponding iterated correction schemes for this kind of equations.The superconvergemceof the numerical solutions of these two algorithms is proved. Not only are the results concerning the Hammersteinintegral equations generalized to nonlinear Fredilolm equations of the second kind, but also more precise resultsare obtained by tising the wavelet method.
文摘In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R^+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
文摘In this paper, a Darbao type random fixed point theorem for a system of weak continuous random operators with random domain is first proved. When, by using the theorem, some existence criteria of random solutions for a systems of nonlinear random Volterra integral equations relative to the weak topology in Banach spaces are given. As applications, some existence theorems of weak random solutions for the random Cauchy problem of a system of nonlinear random differential equations are obtained, as well as the existence of extremal random solutions and random comparison results for these systems of random equations relative to weak topology in Banach spaces. The corresponding results of Szep, Mitchell-Smith, Cramer-Lakshmikantham, Lakshmikantham-Leela and Ding are improved and generalized by these theorems.
文摘In this paper, the existence and uniqueness of the solution of Fredholm-Volterra integral equation is considered (NF-VIE) with continuous kernel;then we used a numerical method to reduce this type of equations to a system of nonlinear Volterra integral equations. Runge-Kutta method (RKM) and Bolck by block method (BBM) are used to solve the system of nonlinear Volterra integral equations of the second kind (SNVIEs) with continuous kernel. The error in each case is calculated.
文摘In this paper, one class of nonlinear singular integral equation is discussed through Lagrange interpolation method. We research the connections between numerical solutions of the equations and chaos in the process of solving by iterative method.
文摘A complete boundary integral formulation for steady compressible inviscid flows governed by nonlinear equations is established by using ρV as variable. Thus, the dimensionality of the problem to be solved is reduced by one and the computational mesh to be generated is needed only on the boundary of the domain.
