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arXiv · 1703.09115

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

Alberto Cabada·Lorena Saavedra
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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.

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Alberto Cabada, Lorena Saavedra. 2017-03-27. Existence of solutions for $n^\mathrm{th}$-order nonlinear differential boundary value problems by means of new fixed point theorems. https://arxiv.org/abs/1703.09115

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