Existence of Three Solutions for a Degenerate Kirchhoff–Type Transmission Problem

Abstract

In this article, we establish the existence of three weak solutions for a nonlinear transmission problem involving degenerate nonlocal coefficients of p(x)–Kirchhoff–type. Our approach is of variational nature; the weak formulation takes place in suitable variable exponent Sobolev spaces.

Keywords:

• Critical point
• Degenerate Kirchhoff–type problem
• Nonlinear transmission problem
• p(x)–Laplacian

Mathematics Subject Classification:

• 35J50
• 35J57

Acknowledgments

Because of a surprising coincidence of names within the same department, we have to point out that F. Cammaroto was born on August 4, 1968.

Part of the special issue, “Variational Analysis and Applications.”