Existence of ground state solutions for a class of bi-non-local Kirchhoff-type problems with variable exponents

Abstract

Our goal in this work is to investigate the existence of ground state solutions, i.e., solutions with the least energy, for a bi-nonlocal Kirchhoff-type problem with variable exponents on compact Riemannian manifolds. Using a minimization argument combined with a quantitative deformation lemma and Brouwer degree theory, we establish the existence of solutions for the problem under consideration.

Keywords

• Kirchhoff-type problem
• Compact riemannian manifolds
• Ground state solutions
• Minimization argument
• Quantitative deformation lemma
• Brouwer degree theory