Zhou Qing-Mei and Wang Ke-Qi: Infinitely many weak solutions for p(x)-Laplacian-like problems with sign-changing potential. (2020)
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Abstract
This study is concerned with the p(x)-Laplacian-like problems and arising from capillarity phenomena of the following type −div ��1 + |∇u| p(x) 1+|∇u| 2p(x) |∇u| p(x)−2∇u = λ f(x, u), in Ω, u = 0, on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, p ∈ C(Ω), and the primitive of the nonlinearity f of super-p + growth near infinity in u and is also allowed to be sign-changing. Based on a direct sum decomposition of a space W 1,p(x) 0 (Ω), we establish the existence of infinitely many solutions via variational methods for the above equation. Furthermore, our assumptions are suitable and different from those studied previously.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 10 |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2020.1.10 |
| Uncontrolled Keywords: | Differenciálegyenlet |
| Additional Information: | Bibliogr.: p. 13-14. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Jun. 08. 09:07 |
| Last Modified: | 2021. Oct. 20. 13:52 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/69514 |
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