Study of a non local elliptic transmission system with singular weights

Abstract

This paper investigates the multiplicity of weak solutions for a transmission problem governed by a coupled system of two nonlinear equations of p(x)-Kirchhoff type. Under nonstandard growth conditions, we establish the existence of at least two distinct non-trivial weak solutions. The proof relies on a variational approach, combining the classical Mountain Pass Theorem with Ekeland's Variational Principle to overcome the lack of regularity inherent to the problem.