The paper considers a scalar linear differential difference equation （LDDE） of mixed type x（t） = （a0 ＋ a1t）X（t） ＋ （b0 ＋ b1t）x（t - 1） ＋ （d0 ＋ d1tx（t ＋ 1） ＋ f（t）, t ∈ R, （＊） where f（t） = ∑...The paper considers a scalar linear differential difference equation （LDDE） of mixed type x（t） = （a0 ＋ a1t）X（t） ＋ （b0 ＋ b1t）x（t - 1） ＋ （d0 ＋ d1tx（t ＋ 1） ＋ f（t）, t ∈ R, （＊） where f（t） = ∑n=0^F fn^tn. This equation is investigated with the use of the method of polynomial quasisolutions based on the representation of an unknown function in the form of polynomial x（t） = ∑n=0^N xn^tn. As a result of substitution of this function into equation （＊）, there appears a residual △（t） = 0（t^N）, for which an exact analytical representation has been obtained. In turn, this allows one to find the unknown coefficients xn and consequently the polynomial quasisolution x（t）. Several examples are considered.展开更多
Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differenti...Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.展开更多
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admi...This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.展开更多
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible ...This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.展开更多
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution an...This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.展开更多
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the sol...This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.展开更多
文摘The paper considers a scalar linear differential difference equation （LDDE） of mixed type x（t） = （a0 ＋ a1t）X（t） ＋ （b0 ＋ b1t）x（t - 1） ＋ （d0 ＋ d1tx（t ＋ 1） ＋ f（t）, t ∈ R, （＊） where f（t） = ∑n=0^F fn^tn. This equation is investigated with the use of the method of polynomial quasisolutions based on the representation of an unknown function in the form of polynomial x（t） = ∑n=0^N xn^tn. As a result of substitution of this function into equation （＊）, there appears a residual △（t） = 0（t^N）, for which an exact analytical representation has been obtained. In turn, this allows one to find the unknown coefficients xn and consequently the polynomial quasisolution x（t）. Several examples are considered.
文摘Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained.
基金Project supported by the NSFC (10971019)Scientific Research Fund of Guangxi Education Department (201012MS067)USM Grant No.12.09.05
文摘This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality. The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained.
基金NNSF of China Grant No.10671211Hu'nan Provincial NSF Grant No.07JJ3005the Scientific and Technical Research Council (TUBITAK) of Turkey
文摘This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation. The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients. It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence. Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
基金Supported by the National Natural Science Foundation of China (No.10971019)Guangxi Natural Science Foundation (No.2010GXNSFA013114)
文摘This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
基金supported by the National Natural Science Foundation of China(No.10971019)the GuangxiProvincial Natural Science Foundation of China(No.2010GXNSFA013114)
文摘This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.
