Infinitely many solutions for anisotropic variable exponent problems

Abstract

We study the existence of infinitely many solutions for anisotropic variable exponent problem of the type

with the Neumann boundary condition. Here, f is a Carathéodory function and are continuous functions on with . We show the existence of infinitely many solutions for suitable range of by analyzing the critical points of the Euler functional. We also study some corollaries of the main results and finally present some examples.

Keywords:

• Neumann problem
• critical points
• weak solutions
• anisotropic variable exponent problems

AMS Subject Classifications:

• 34B15
• 35B38
• 58E05

Notes

No potential conflict of interest was reported by the authors.