Lima Alves Ricardo and Reis Mariana: About existence and regularity of positive solutions for a quasilinear Schrödinger equation with singular nonlinearity. (2020)
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Abstract
We establish the existence of positive solutions for the singular quasilinear Schrödinger equation −∆u − ∆(u 2 )u = h(x)u −γ + f(x, u) in Ω, u(x) = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 3) is a bounded domain with smooth boundary ∂Ω, 1 < γ, h ∈ L 1 (Ω) and h > 0 almost everywhere in Ω. The function f may change sign on Ω. By using the variational method and some analysis techniques, the necessary and sufficient condition for the existence of a solution is obtained.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 60 |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2020.1.60 |
| Uncontrolled Keywords: | Differenciálegyenlet, Schrödinger egyenlet |
| Additional Information: | Bibliogr.: p. 21-23. ; összefoglalás angol nyelven |
| Date Deposited: | 2020. Dec. 01. 08:28 |
| Last Modified: | 2021. Oct. 20. 13:52 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/70944 |
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