Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

Abstract

We study the existence of solutions for nonlinear boundary value problemsφu′′=ft,u,u′,  lu,u′=0, wherel(u,u′)=0denotes the boundary conditions on a compact interval0,T,φis a homeomorphism such thatφ(0)=0, andf:0,T×R×R→Ris 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.