Existence of infinitely many solutions for fractional p-Laplacian equations with sign-changing potential

Abstract

In this article, we prove the existence of infinitely many solutions for the fractional $p$-Laplacian equation $$ (-\Delta)^s_p u+V(x)|u|^{p-2}u=f(x,u),\quad x\in \mathbb{R}^N $$ where $s\in(0,1)$, $2\leq p<\infty$. Based on a direct sum decomposition of a space $E^s$, we investigate the multiplicity of solutions for the fractional p-Laplacian equation in $\mathbb{R}^N$. The potential V is allowed to be sign-changing, and the primitive of the nonlinearity f is of super-p growth near infinity in u and allowed to be sign-changing. Our assumptions are suitable and different from those studied previously.

Keywords

• Fractional p-Laplacian
• multiple solutions
• variational methods
• sign-changing potential