Existence of Solutions for Some Nonlinear Problems with Boundary Value Conditions

Abstract EN

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 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.