In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random vari...In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case.展开更多
The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the...The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.展开更多
In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Bot...In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.展开更多
This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate ...This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.展开更多
The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that...The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that g grows superlinearly and p grows with respect to u and u′ linearly at most, the boundary value problem has an infinitude of solutions.展开更多
This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
The existence of solutions is obtained for a class of the non-periodic SchrSdinger equation -△u ＋ V（x）u = f（x,u）, x E RN, by the generalized mountain pass theorem, where V is large at infinity and f is superline...The existence of solutions is obtained for a class of the non-periodic SchrSdinger equation -△u ＋ V（x）u = f（x,u）, x E RN, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as ｜u｜→ ∞.展开更多
In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other t...In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition., the method is globally and superlinearly convergent.展开更多
In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with...In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.展开更多
By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,...By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.展开更多
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed poi...In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.展开更多
A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assum...A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.展开更多
A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)｜x(t)｜αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous f...A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)｜x(t)｜αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous functions on[t0,∞). This criterion extends and unifies some of the results obtained in [1]- [5].展开更多
It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the ...It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).展开更多
The cone theorem and the fixed point index are used to investigate the positive solution of singular superlinear boundary value problem for a fourth order nonlinear differential equation.
This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method fo...This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.展开更多
文摘In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case.
基金supported by Doctoral Scientific Research Starting Foundation of Jingdezhen Ceramic University(Grant No.102/01003002031)Re-accompanying Funding Project of Academic Achievements of Jingdezhen Ceramic University(Grant Nos.215/20506277,215/20506341)。
文摘The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space.
文摘In this paper,we prove the existence of martingale solutions of a class of stochastic equations with a monotone drift of polynomial growth of arbitrary order and a continuous diffusion term with superlinear growth.Both the nonlinear drift and diffusion terms are not required to be locally Lipschitz continuous.We then apply the abstract result to establish the existence of martingale solutions of the fractional stochastic reaction-diffusion equation with polynomial drift driven by a superlinear noise.The pseudo-monotonicity techniques and the Skorokhod-Jakubowski representation theorem in a topological space are used to pass to the limit of a sequence of approximate solutions defined by the Galerkin method.
基金supported by the National Natural Science Foundation of China(No.12271399)the Fundamental Research Funds for the Central Universities(No.3122025090)。
文摘This paper investigates global solutions and long-time dynamics for the stochastic reaction-diffusion equation du=(Δu+f(u)+g(x,t))dt+σ(u)dW on a bounded domain,where the drift term f(u),with polynomial growth rate β,is strongly dissipative and the diffusion term σ(u)has growth rate γ,satisfying β+1>2γ.Under this condition,we establish the existence,uniqueness,and regularity of solutions in Bochner spaces.Our analysis relies only on weak monotonicity conditions and requires no further growth restrictions on f andσ.Moreover,we prove the existence of a weak mean random attractor for the system.These results offer new insights into the balance mechanism between stochastic perturbations and dissipative effects in superlinear regimes.
文摘The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that g grows superlinearly and p grows with respect to u and u′ linearly at most, the boundary value problem has an infinitude of solutions.
文摘This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.
基金supported by the National Natural Science Foundation of China(11171262)the Specialized Research Fund for the Doctoral Program of Higher Education (200804860048)
文摘We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.
基金Supported by National Natural Science Foundation of China(11071198)Doctor Research Foundation of Southwest University of Science and Technology (11zx7130)the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province(D20112605)
文摘The existence of solutions is obtained for a class of the non-periodic SchrSdinger equation -△u ＋ V（x）u = f（x,u）, x E RN, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as ｜u｜→ ∞.
文摘In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition., the method is globally and superlinearly convergent.
文摘In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
基金Foundation item： Supported by the National Natural Science Foundation of China（10671167） Supported by the Research Foundation of Liaocheng University（31805）
文摘By applying fixed point theorem, the existence of positive solution is considered for superlinear semipositone singular m-point boundary value problem -（Lφ）（x）=（p（x）φ′（x））′＋q（x）φ（x） and ξi ∈ （0,1）with 0〈ξ1〈ξ2……〈ξm-2〈1,αi ∈ R^＋,f ∈C[（0,1）×R^＋,R^＋],f（x,φ） may be singular at x=0 and x=1,g（x）：（0,1）→R is Lebesgue measurable, g may tend to negative infinity and have finitely many singularities.
文摘In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.
基金Supported by the National Natural Science Foundation of P.R.China(1 9971 0 0 2 ) and the Subject ofBeijing Educational Committ
文摘A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.
文摘A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)｜x(t)｜αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous functions on[t0,∞). This criterion extends and unifies some of the results obtained in [1]- [5].
基金This research is supported by NNSFC(1 9771 0 72 ) and ZNSF.And thanks to JNCASR in India Fortheir host when the firstauthor is
文摘It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).
基金Sponsored by the National Natural Science Foundation of China (Grant No.10271034).
文摘The cone theorem and the fixed point index are used to investigate the positive solution of singular superlinear boundary value problem for a fourth order nonlinear differential equation.
基金supported by the National Natural Science Foundation of China(12171106)the Natural Science Foundation of Guangxi Province(2020GXNSFDA238017 and 2018GXNSFFA281007)the Shanghai Sailing Program(21YF1430300)。
文摘This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.
