Wang Li and Wang Jixiu and Li Xiongzheng: Infinitely many solutions to quasilinear Schrödinger equations with critical exponent. (2019)
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Abstract
This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: −∆pu + V(x)|u| p−2u − ∆p(|u| 2ω)|u| 2ω−2u = ak(x)|u| q−2u + b|u| 2ωp ∗−2u, x ∈ R N. Here ∆pu = div(|∇u| p−2∇u) is the p-Laplacian operator with 1 < p < N, p N p N−p is the critical Sobolev exponent. 1 ≤ 2ω < q < 2ωp, a and b are suitable positive parameters, V ∈ C(RN, [0, ∞)), k ∈ C(RN, R). With the help of the concentration-compactness principle and R. Kajikiya’s new version of symmetric Mountain Pass Lemma, we obtain infinitely many solutions which tend to zero under mild assumptions on V and k.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2019 |
| Number: | 5 |
| ISSN: | 1417-3875 |
| Page Range: | pp. 1-16 |
| DOI: | 10.14232/ejqtde.2019.1.5 |
| Uncontrolled Keywords: | Schrödinger egyenlet |
| Additional Information: | Bibliogr.: p. 14-16. ; összefoglalás angol nyelven |
| Date Deposited: | 2019. May. 31. 07:15 |
| Last Modified: | 2021. Sep. 16. 10:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/58112 |
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