SEMICLASSICAL STATES FOR THE PSEUDO-RELATIVISTIC SCHRODINGER EQUATION WITH COMPETING POTENTIALS

journal article in Web of Science

English

n this paper, we establish concentration and multiplicity properties of positive ground state solutions to the following perturbed pseudo-relativistic Schrödinger equation with competing potentials where N >2s, ϵ is a small positive parameter, and (−Δ+m2)s is the pseudo-relativistic Schrödinger operator with s∈(0,1) and mass m>0. We assume that the potentials V, K and the nonlinearity f are continuous but are not necessarily of class C1. Under natural hypotheses, combining the extension method, Nehari analysis and the Ljusternik-Schnirelmann category theory, we first study the existence and concentration phenomena of positive solutions for ϵ>0 sufficiently small, as well as multiplicity properties depending on the topology of the set where V attains its global minimum and K attains its global maximum. Moreover, we establish the asymptotic convergence and the exponential decay of positive solutions. In the final part of this paper, we provide a sufficient condition for the non-existence of ground state solutions.

concentration; ground states; multiplicity; Pseudo-relativistic Schrödinger equation

RADULESCU, V.; ZHANG, W.; ZHANG, J.

20. 3. 2025

1539-6746

Communications in Mathematical Sciences

23

2

United States of America

465

507

43

https://dx.doi.org/10.4310/CMS.241217220205