Multiple solutions for a fractional p-Laplacian equation with sign-changing potential

• Main Author: Vincenzo Ambrosio
• Format: Article
• Language: English
• Published: Texas State University 2016-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Fractional p-Laplacian; sign-changing potential; fountain theorem
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/151/abstr.html

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the fractional p-Laplace equation $$\displaylines{ (-\Delta)_p^s u + V(x) |u|^{p-2}u = f(x, u) \quad \text{in } \mathbb{R}^N, }$$ where $s\in (0,1)$, $p\geq 2$, $N\geq 2$, $(- \Delta)_{p}^s$ is the fractional p-Laplace operator, the nonlinearity f is p-superlinear at infinity and the potential V(x) is allowed to be sign-changing.