Abstract

In this article, we study the existence and multiplicity of weak solutions for a class of elliptic Navier boundary value problems involving the $(p_{1}(\cdot),p_{2}(\cdot))$-biharmonic operator. Our technical approach is based on variational methods and the theory of the variable exponent Lebesgue spaces. We establish the existence of at least one solution and infinitely many solutions of this problem, respectively.

Keywords: $p_{1}(\cdot)$-Laplacian; mountain pass theorem; multiple solutions; critical point theory.

MSC: 39A05, 34B15

Pages:  196$-$206     

Volume  72 ,  Issue  3 ,  2020