Szczegóły publikacji
Opis bibliograficzny
Multiple solutions of double phase variational problems with variable exponent / Xiayang Shi, Vicenţiu D. RǍDULESCU, Dušan D. Repovš, Qihu Zhang // Advances in Calculus of Variations ; ISSN 1864-8258. — 2020 — vol. 13 iss. 4, s. 385–401. — Bibliogr., Abstr. — Publikacja dostępna online od: 2018-06-16. — V. Rǎdulescu – dod. afiliacje: Institute of Mathematics, Physics and Mechanics, Ljubljana; University of Craiova
Autorzy (4)
- Shi Xiayang
- AGHRǎdulescu Vicenţiu
- Repovš Dušan D.
- Zhang Qihu
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 130835 |
|---|---|
| Data dodania do BaDAP | 2020-10-30 |
| DOI | 10.1515/acv-2018-0003 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Advances in Calculus of Variations |
Abstract
This paper deals with the existence of multiple solutions for the quasilinear equation -div A(x, del u) + vertical bar u vertical bar(alpha(x)-2)u = f(x, u) in R-N, which involves a general variable exponent elliptic operator A in divergence form. The problem corresponds to double phase anisotropic phenomena, in the sense that the differential operator has various types of behavior like vertical bar xi vertical bar(q(x)-2) xi' for small vertical bar xi vertical bar and like vertical bar xi vertical bar(p(x)-2)xi. for large vertical bar xi vertical bar, where 1 < alpha(center dot) <= p(center dot) < q(center dot) < N. Our aim is to approach variationally the problem by using the tools of critical points theory in generalized Orlicz—–Soboley spaces with variable exponent. Our results extend the previous works [A. Azzollini, P. d'Avenia and A. Pomponio, Quasilinear elliptic equations in R-N via variational methods and Orlicz-Sobolev embeddings, Cale. Var. Partial Differential Equations 49 (201/), no. 1-2,197-213] and [N. Chorfi and V. U. Radulescu, Standing wave solutions of a quasilinear degenerate Schrodinger equation with unbounded potential, Electron. I. Qual. Theory Differ. Equ. 2016 (2016), Paper No. 37] from cases where the exponents p and q are constant, to the case where p(center dot) and q(center dot) are functions. We also substantially weaken some of the hypotheses in these papers and we overcome the lack of compactness by using the weighting method.
