Szczegóły publikacji
Opis bibliograficzny
Planar Schrödinger equations with critical exponential growth / Sitong Chen, Vicenţiu D. RǍDULESCU, Xianhua Tang, Lixi Wen // Calculus of Variations and Partial Differential Equations ; ISSN 0944-2669. — 2024 — vol. 63 iss. 9 art. no. 243, s. 1–46. — Bibliogr. s. 44–46, Abstr. — Publikacja dostępna online od: 2024-11-11. — V. D. Rǎdulescu – dod. afiliacja: Brno University of Technology, Faculty of Electrical Engineering and Communication, Czech Republic; Department of Mathematics, University of Craiova, Romania; School of Mathematics, Zhejiang Normal University, China; Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Autorzy (4)
- Chen Sitong
- AGHRǎdulescu Vicenţiu
- Tang Xianhua
- Wen Lixi
Dane bibliometryczne
| ID BaDAP | 157193 |
|---|---|
| Data dodania do BaDAP | 2024-12-12 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s00526-024-02852-z |
| Rok publikacji | 2024 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Calculus of Variations and Partial Differential Equations |
Abstract
In this paper, we study the following quasilinear Schrödinger equation: (Formula presented.) where ε>0 is a small parameter, V∈C(R2,R) is uniformly positive and allowed to be unbounded from above, and g∈C(R,R) has a critical exponential growth at infinity. In the autonomous case, when ε>0 is fixed and V(x)≡V0∈R+, we first present a remarkable relationship between the existence of least energy solutions and the range of V0 without any monotonicity conditions on g. Based on some new strategies, we establish the existence and concentration of positive solutions for the above singularly perturbed problem. In particular, our approach not only permits to extend the previous results to a wider class of potentials V and source terms g, but also allows a uniform treatment of two kinds of representative nonlinearities that g has extra restrictions at infinity or near the origin, namely lim inf|t|→+∞tg(t)eα or g(u)≥Cq,Vuq-1 with q>4 and Cq,V>0 is an implicit value depending on q, V and the best constant of the embedding H1(R2)⊂Lq(R2), considered in the existing literature. To the best of our knowledge, there have not been established any similar results, even for simpler semilinear Schrödinger equations. We believe that our approach could be adopted and modified to treat more general elliptic partial differential equations involving critical exponential growth.
