Multiplicity and concentration results for some nonlinear Schrödinger equations with the fractional $p$-Laplacian

Abstract

We consider a class of parametric Schrödinger equations driven by the fractional $p$-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth. By using variational methods and Ljusternik-Schnirelmann theory, we study the existence, multiplicity and concentration of positive solutions for small values of the parameter.

References in corpus (2)

• A Hopf's lemma and a strong minimum principle for the fractional $p$-Laplacian
• Ground state solutions for a fractional Schrödinger equation with critical growth

Cited by in corpus (7)

• Multiplicity and concentration results for a $(p,q)$-Laplacian problem in ${\mathbb{R}}^N$
• Eigenvalues for a combination between local and nonlocal $p-$Laplacians
• Spectrum of the fractional $p-$Laplacian in ${\mathbb{R}}^N$ and decay estimate for positive solutions of a Schrödinger equation
• Existence, multiplicity and concentration for a class of fractional $p\&q$ Laplacian problems in ${\mathbb{R}}^N$
• Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
• Multiple solutions for a fractional Schrodinger equation with potentials
• On the multiplicity and concentration of positive solutions for a $p$-fractional Choquard equation in ${\mathbb{R}}^N$