Existence of solutions for nth-order nonlinear differential boundary value problems by means of fixed point theorems. (August 2018)

• Record Type: Journal Article
• Authors: Cabada, Alberto; Saavedra, Lorena
• Is Part Of: Nonlinear analysis. Volume 42(2018)
• Page Start: 180
• Page End: 206
• Publication Date: 2018-08
• Subjects: Green's functions -- Fixed point theorems -- Nonlinear boundary value problems; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.12.008
• Languages: English
• ISSNs: 1468-1218

Abstract

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 Krasnoselskiĭ'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.