Existence results of infinitely many solutions for a class of p(x)-biharmonic problems

Shokooh, Saeid; Alizadeh Afrouzi, Ghasem

Existence results of infinitely many solutions for a class of p(x)-biharmonic problems

Document Type : Research Paper

Authors

¹ Department of Mathematics, Faculty of Sciences, Gonbad Kavous University, Gonbad Kavous, Iran

² Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$-biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.

Keywords