Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth

Authors

  • Nguyen Van Thin Thai Nguyen University of Education, Department of Mathematics, and Thang Long University, Thang Long Institute of Mathematics and Applied Sciences

Keywords:

Critical exponential growth, fractional p-Laplace, Ljusternik-Schnirelmann theory, Mountain Pass Theorem, Trudinger-Moser inequality, variational method

Abstract

 

In this paper, we study the Schrödinger equation involving Ns-fractional Laplace as follows εN(Δ)N/ssu+V(x)|u|Ns2u=f(u) in RN, where ε is a positive parameter, N=ps, s(0,1). The nonlinear function f has the exponential growth and potential function V is a continuous function satisfying some suitable conditions. Our problem lacks of compactness. By using the Ljusternik-Schnirelmann theory, we obtain the existence, multiplicity and concentration of nontrivial nonnegative solutions for small values of the parameter.

 

Section
Articles

Published

2022-03-24

How to Cite

Thin, N. V. (2022). Multiplicity and concentration of solutions to a fractional p-Laplace problem with exponential growth. Annales Fennici Mathematici, 47(2), 603–639. https://doi.org/10.54330/afm.115564