About existence and regularity of positive solutions for a quasilinear Schrödinger equation with singular nonlinearity
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...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2020
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet, Schrödinger egyenlet |
| doi: | 10.14232/ejqtde.2020.1.60 |
| Online Access: | http://acta.bibl.u-szeged.hu/70944 |
| Tartalmi kivonat: | 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. |
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| ISSN: | 1417-3875 |