Existence of solutions for some nonlinear problems with boundary value conditions

2016/06/01 by Santos, Dionicio Pastor Dallos
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.00078

Abstract

In this paper we study the existence of solutions for nonlinear boundary value problems (ϕ(u' ))' = f(t,u,u'), l(u,u')=0 where l(u,u') =0 denotes the Dirichlet or mixed conditions on [0, T], ϕ is a bounded, singular or classic homeomorphism such that ϕ(0)=0, f(t,x,y) is a continuous function, and T a positive real number. All the contemplated boundary value problems are reduced to finding a fixed point for one operator defined on a space of functions, and Schauder fixed point theorem or Leray-Schauder degree are used.

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