Nonlinear boundary value problems of a class of elliptic equations involving critical variable exponents

Abstract

Abstract In this paper, we first obtain the existence of solutions for a class of elliptic equations involving critical variable exponents and nonlinear boundary values by the mountain pass theorem and concentration compactness principle. Then, under suitable assumptions, we obtain a sequence of solutions with positive energies going towards infinity by Fountain Theorem.

Keywords

• Variable exponent Sobolev space
• Weak solution
• Mountain pass theorem
• Fountain Theorem
• Variational method