Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

Abstract

We study the existence of solutions for nonlinear boundary value problems φu′′=ft,u,u′, lu,u′=0, where l(u,u′)=0 denotes the boundary conditions on a compact interval 0,T, φ is a homeomorphism such that φ(0)=0, and f:0,T×R×R→R is a continuous function. 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 is used.