On the solvability of nonlinear boundary value problems

On the Solvability of Nonlinear, First-Order Boundary Value Problems

This article investigates the existence of solutions to first-order, nonlinear boundary value problems (BVPs) involving systems of ordinary differential equations and two-point boundary conditions. Some sufficient conditions are presented that will ensure solvability. The main tools employed are novel differential inequalities and fixed-point methods. AMS 2000 Classification: 34B15, 34B99

Solvability for second order nonlinear impulsive boundary value problems

Impulsive differential equations play a very important role in understanding mathematical models of real processes and phenomena studied in physics, chemical technology, population dynamics, biotechnology, economics and so on, see [1,2,8,10,17]. About wide applications of the theory of impulsive differential equations to different areas, we refer the readers to monographs [5,7,18,19] and the re...

Solvability of Nonlocal Fractional Boundary Value Problems

On the Solvability of Periodic Boundary Value Problems with Impulse

In this work we obtain some new results concerning the existence of solutions to an impulsive first-order, nonlinear ordinary differential equation with periodic boundary conditions. The ideas involve differential inequalities and Schaefer's fixed-point theorem.

Solvability of discrete Neumann boundary value problems

In this article we gain solvability to a nonlinear, second-order difference equation with discrete Neumann boundary conditions. Our methods involve new inequalities on the right-hand side of the difference equation and Schaefer’s Theorem in the finite-dimensional space setting. © 2006 Elsevier Inc. All rights reserved.