English

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

Analysis of PDEs 2017-03-07 v3

Abstract

We use a variant of the fountain Theorem to prove the existence of infinitely many weak solutions for the following fractional p-Laplace equation (-\Delta)^{s}_{p}u+V(x)|u|^{p-2}u=f(x,u) in R^N, where s(0,1)s \in (0,1),p2 p \geq 2,N2 N \geq 2, (Δ)ps(-\Delta)^{s}_{p} is the fractional pp-Laplace operator, the nonlinearity f is pp-superlinear at infinity and the potential V(x) is allowed to be sign-changing.

Keywords

Cite

@article{arxiv.1603.05282,
  title  = {Multiple solutions for a fractional $p$-Laplacian equation with sign-changing potential},
  author = {Vincenzo Ambrosio},
  journal= {arXiv preprint arXiv:1603.05282},
  year   = {2017}
}
R2 v1 2026-06-22T13:12:42.590Z