A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalizati...A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalization of the classical monotone iteration theory for continuous problems.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
In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower...In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.展开更多
This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with r...This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.展开更多
The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsi...This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.展开更多
Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with...Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.展开更多
The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied....The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.展开更多
In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and perio...In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β展开更多
This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mi...This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.展开更多
This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is pres...This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.展开更多
In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z...In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z2),x∈R^(N),where G is a nonlinear operator and Sk(λ(D^(2)z))stands for the k-Hessian operator.We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system ifφ(|x|,z1,z2)=b(|x|)φ(z1,z2)andψ(|x|,z1,z2)=h(|x|)ψ(z1).Moreover,with the help of the monotone iterative method,some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearitiesψ,φare given,which improve and extend many previous works.展开更多
In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain exist...In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .展开更多
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an ...The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.展开更多
In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=...In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.展开更多
We apply the method of lower and upper solutions combined with mono- tone iterations to fractional differential problem with a parameter. The existence of minimal and maximal solutions is proved for the fractional dif...We apply the method of lower and upper solutions combined with mono- tone iterations to fractional differential problem with a parameter. The existence of minimal and maximal solutions is proved for the fractional differential problem with a parameter.展开更多
In this paper,boundary value problems(BVP for short) for second order singular differential equations are reduced to initial value problems(IVP for short)for first order singular integro-differential equations and the...In this paper,boundary value problems(BVP for short) for second order singular differential equations are reduced to initial value problems(IVP for short)for first order singular integro-differential equations and the existence of external solutions of reduction IVP is given,in which f is increasing in the integral term,and thus one can obtain existence of solutions of second order problems.展开更多
文摘A monotone iterative method for some discontinuous variational boundary problems is given, the convergence of iterative solutions is proved by the theory of partially ordered sets. It can be regarded as a generalization of the classical monotone iteration theory for continuous problems.
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.
文摘In this paper, the existence of solutions for discontinuous nonlinear parabolic differential IBVP is proved by using a more generalized monotone iterative method. Moreover, the convergence of this method is discussed.
基金National Natural Science Foundation of China(No.11271372)Hunan Provincial National Natural Science Foundation of China(No.12JJ2004)Central South University Graduate Innovation Project,China(No.2014zzts136)
文摘In this paper,the existence and uniqueness of iterative solutions to the boundary value problems for a class of first order impulsive integro-differential equations were studied. Under a new concept of upper and lower solutions, a new monotone iterative technique on the boundary value problem of integro-differential equations was proposed. The existence and uniqueness of iterative solutions and the error estimation in certain interval were obtained.An example was also given to illustrate the results.
文摘This paper deals with fractional integro-differential equations involving Hadamard fractional derivatives and nonlinear boundary conditions in an ordered Banach space. The nonlinearity is allowed to be singular with respect to time variable. Under some monotonicity conditions and noncompactness measure conditions, we use the method of coupled lower and upper L-quasisolutions associated with the mixed monotone iterative technique to investigate the existence of extremal L-quasisolutions. A unique solution between coupled lower and upper L-quasisolutions is also obtained. An example is given to illustrate our theoretical results. The results got in this paper are new and enrich the existing related work.
文摘The objective of this paper is to develop monotone techniques for obtaining extremal solutions of initial value problem for nonlinear neutral delay differential equations.
文摘This paper uses the method of upper and lower solutions and the monotone iterative technique to investigate the existence of maximal and minimal solutions of the periodic boundary value problem for first order impulsive functional differential equations.
基金the National Natural Science Foundation of China(No.10671060)the Doctoral Fund of Ministry of Education of China granted[2003]0532006
文摘Some block iterative methods for solving variational inequalities with nonlinear operators are proposed. Monotone convergence of the algorithms is obtained. Some comparison theorems are also established. Compared with the research work in given by Pao in 1995 for nonlinear equations and research work in given by Zeng and Zhou in 2002 for elliptic variational inequalities, the algorithms proposed in this paper are independent of the boundedness of the derivatives of the nonlinear operator.
基金Supported by the Natural Science Foundation of Zhejiang Province (Y605144)the XNF of Zhejiang University of Media and Communications (XN080012008034)
文摘The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″(t) + q(t)f(t,u(t),u′(t)) = 0, 0 〈 t 〈 1, u(0) = u″(0) = u′(1) = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.
文摘In this paper, we show that the method of monotone iterative technique is valid to obtain two monotone sequences that converge uniformly to extremal solutions to second order periodic boundary value problems and periodic solutions of functional difference equations. We obtain some new results under the lower solution α and upper solutionβ with α≤β
文摘This paper studies the existence of solutions for mixed monotone impulsive Volterra integral equations on the infinite interval R+ with an infinite number of moments of impulse effect in Banach spaces. By using the mixed monotone iterative technique and Monch fixed point theorem, Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. Finally, an example is worked out.
基金Supported by the National Natural Science Foundation of China (10571050 10871062)Hunan Provincial Innovation Foundation For Postgraduate
文摘This paper is concerned with the existence and approximation of solutions for a class of first order impulsive functional differential equations with periodic boundary value conditions. A new comparison result is presented and the previous results are extended.
基金Supported by the National Natural Science Foundation of China(11501342,12001344).
文摘In this paper,we consider the following generalized nonlinear k-Hessian system G(S_(k)^(1/k)(λ(D^(2)z1)))S_(k)^(1/k)(λ(D^(2)z1))=φ(|x|,z1,z2),x∈R^(N),G(S_(k)^(1/k)(λ(D^(2)z2)))S_(k)^(1/k)(λ(D^(2)z2))=ψ(|x|,z1,z2),x∈R^(N),where G is a nonlinear operator and Sk(λ(D^(2)z))stands for the k-Hessian operator.We first are interested in the classification of positive entire k-convex radial solutions for the k-Hessian system ifφ(|x|,z1,z2)=b(|x|)φ(z1,z2)andψ(|x|,z1,z2)=h(|x|)ψ(z1).Moreover,with the help of the monotone iterative method,some new existence results on the positive entire k-convex radial solutions of the k-Hessian system with the special non-linearitiesψ,φare given,which improve and extend many previous works.
文摘In this paper, the following initial value problem for nonlinear integro-differential equationis considered , whereUsing the method of upper and lower solutions and the monotone iterative technique .We obtain existence results of minimal and maximal solutions .
文摘This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘The existence and iteration of positive solution for classical Gelfand models are considered, where the coefficient of nonlinear term is allowed to change sign in [0, 1]. By using the monotone iterative technique, an existence theorem of positive solution is obtained, corresponding iterative process and convergence rate are given. This iterative process starts off with zero function, hence the process is simple, feasible and effective.
基金supported by NSFC(12001344)the Graduate Education and Teaching Innovation Project of Shanxi,China(2021YJJG142)+1 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0123)the Technology Research Foundation of Chongqing Educational Committee(KJQN201900539 and KJQN202000528)。
文摘In this paper,we are concerned with the existence of the positive bounded and blow-up radial solutions of the(k1,k2)-Hessian system■where G is a nonlinear operator,Ki=Ski(λ(D^(2) z_(i)))+ψ_(i)(|x|)|▽_(zi)|^(ki),i=1,2.Under the appropriate conditions on gi and g2,our main results are obtained by using the monotone iterative method and the Arzela-Ascoli theorem.Furthermore,our main results also extend the previous existence results for both the single equation and systems.
基金The NSF(11371364)of Chinathe Fundamental Research Funds(2009QS06)for the Cen-tral Universitiesthe 2013 Science and Technology Research Project(KM201310016001)of Beijing Municipal Education Commission
文摘We apply the method of lower and upper solutions combined with mono- tone iterations to fractional differential problem with a parameter. The existence of minimal and maximal solutions is proved for the fractional differential problem with a parameter.
文摘In this paper,boundary value problems(BVP for short) for second order singular differential equations are reduced to initial value problems(IVP for short)for first order singular integro-differential equations and the existence of external solutions of reduction IVP is given,in which f is increasing in the integral term,and thus one can obtain existence of solutions of second order problems.