Existence of solutions for a coupled system with ∅-Laplacian operators and nonlinear coupled boundary conditions

Abstract

Abstract. We study the existence of solutions of the systemsubmitted to nonlinear coupled boundary conditions on [0, T ] where φ1, φ2 : (−a, a) → R, with 0 < a < +∞, are two increasing homeomorphisms such that φ1(0) = φ2(0) = 0, and fi :1 -Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.