Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

Dajun Guo

doi:10.1155/s1048953391000035

Abstract

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

Highlights

In [1], several existence theorems were established for the BVP of nonlinear second order differential equation in Banach space"
Several Lemmas Let E be a real Banach space and P be a cone in E which defines a partial ordering in E by z < y iff y-x P
{z E P(1)" Ilzlll _< R} is a nonempty bounded closed convex set of CI[I,E], Darbo theoremimplies that A has a fixed point in U, which is a solution of (44), and our theorem is proved

Summary

Introduction

ABSTILCT In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. In [1] (see [21 Section 5.3), several existence theorems were established for the BVP of nonlinear second order differential equation in Banach space" In this paper, we shall combine the fixed point theory, fixed point index theory and cone theory to extend some results of [1] to the BVP of nonlinear second order integrodifferential equation of mixed type in Banach space:

Results

Conclusion