Wei Yunfeng and Chen Caisheng and Yang Hongwei and Yu Hongwang: Existence of weak solutions for quasilinear Schrödinger equations with a parameter. (2020)
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Abstract
In this paper, we study the following quasilinear Schrödinger equation of the form −∆pu + V(x)|u| p−2u − h ∆p(1 + u 2 α/2i αu 2(1 + u 2) (2−α)/2 = k(u), x ∈ R N, where p-Laplace operator ∆pu = div(|∇u| p−2∇u) (1 < p ≤ N) and α ≥ 1 is a parameter. Under some appropriate assumptions on the potential V and the nonlinear term k, using some special techniques, we establish the existence of a nontrivial solution in C 1,β loc (RN) (0 < β < 1), we also show that the solution is in L ∞(RN) and decays to zero at infinity when 1 < p < N.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 41 |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2020.1.41 |
| Uncontrolled Keywords: | Schrödinger egyenlet, Differenciálegyenlet, Laplace-operátor |
| Additional Information: | Bibliogr.: p. 18-20. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Dec. 01. 08:45 |
| Last Modified: | 2021. Oct. 20. 13:52 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/70154 |
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