Existence of solutions for $n^{\mathrm{th}}$-order nonlinear differential boundary value problems by means of new fixed point theorems

Abstract

This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow the well-known Krasnoselski\uı's fixed point Theorem together with two fixed point results of Leggett-Williams type. After obtaining a general existence result for a one parameter family of nonlinear differential equations, are proved, as particular cases, existence results for second and fourth order nonlinear boundary value problems.

31 pages, 12 figures

References in corpus (1)

• A positive fixed point theorem with applications to systems of Hammerstein integral equations