Szczegóły publikacji
Opis bibliograficzny
Semiclassical states for the pseudo-relativistic Schrödinger equation with competing potentials / Wen Zhang, Jian Zhang, Vicenţiu D. RǍDULESCU // Communications in Mathematical Sciences ; ISSN 1539-6746. — 2025 — vol. 23 no. 2, s. 465-507. — Bibliogr., Abstr. — Publikacja dostępna online od: 2024-12-17. — V. Rădulescu - dod. afiliacja: Brno University of Technology, Czech Republic; University of Craiova, Romania; "Simion Stoilow" Institute of Mathematics of the Romanian Academy; Zhejiang Normal University, China
Autorzy (3)
- Zhang Wen
- Zhang Jian
- AGHRǎdulescu Vicenţiu
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 162074 |
|---|---|
| Data dodania do BaDAP | 2025-09-08 |
| DOI | 10.4310/CMS.241217220205 |
| Rok publikacji | 2025 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Communications in Mathematical Sciences |
Abstract
In this paper, we establish concentration and multiplicity properties of positive ground state solutions to the following perturbed pseudo-relativistic Schrodinger equation with competing potentials {(-epsilon(2)Delta + m(2))(s)u+ V (x)u = K(x)f(u) in R-N, u is an element of H-s (R-N), u> 0 in R-N, where N > 2s, epsilon is a small positive parameter, and (-Delta + m(2))(s) is the pseudo-relativistic Schrodinger operator with s 2 (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 C 1. 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 epsilon > 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.
