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

Konan Charles Etienne Goli 1  and Assohoun Adjé 2
  • 1 UFR Mathématiques et informatique, Université Félix Houphouet Boigny de Côte D'Ivoire, 22 BP 582 , Abidjan , Côte D'Ivoire
  • 2 FR Mathématiques et informatique, Université Félix Houphouet Boigny de Côte D'Ivoire, 22 BP 582 , Abidjan, Côte D'Ivoire

Abstract

We study the existence of solutions of the system submitted to nonlinear coupled boundary conditions on [0, T] where ∅1,2: (-a, a) → ℝ, with 0 < a < +∞, are two increasing homeomorphisms such that ∅1(0) = ∅2(0) = 0, and fi : [0, T] × ℝ4 → ℝ, i ∈{1, 2} are two L1-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

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