Special Session 1: Analysis of PDEs and Free Boundary Problems

Multiplicity and concentration results for some nonlinear Schr\odinger equations with the fractional $p$-Laplacian

Teresa Isernia
Universit\`a Politecnica delle Marche
Italy
Co-Author(s):    
Abstract:
We consider a class of parametric Schr\odinger 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.