We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing...We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.展开更多
This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth s...This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth solutions on [0, ∞] are given by constructing new lower and upper solutions.展开更多
Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ ...We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.展开更多
We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.
基金Ministerio de Educacióny Ciencia and FEDER,Project MTM2004-06652-C03-01Xunta de Galicia and FEDER,Projects PGIDIT02PXIC20703PN and PGIDIT05PXIC20702PN
文摘We prove some fixed point theorems in partially ordered sets, providing an extension of the Banach contractive mapping theorem. Having studied previously the nondecreasing case, we consider in this paper nonincreasing mappings as well as non monotone mappings. We also present some applications to first-order ordinary differential equations with periodic boundary conditions, proving the existence of a unique solution admitting the existence of a lower solution.
文摘This paper investigates existence of positive solutions of singular sub-linear boundary value problems on a half-line. Necessary and sufficient conditions for the existence of positive continuous solutions or smooth solutions on [0, ∞] are given by constructing new lower and upper solutions.
文摘Using the method of upper and lower solutions and its associated monotone iterative, consider the existence and uniqueness of solution of an initial value problem for the nonlinear fractional diffusion equation.
基金Project supported by the National Natural Science Foundation of China
文摘We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.
文摘We use the method of lower and upper solutions combined with monotone iterations to differential problems with a parameter. Existence of extremal solutions to such problems is proved.
