Existence of nontrivial solutions for a quasilinear Schrödinger-Poisson system in R3 with periodic potentials
In this paper, we study the following quasilinear Schrödinger–Poisson system in R3 −∆u + V(x)u + λϕu = f(x, u), x ∈ R3 4∆4ϕ = λu 2 , x ∈ R3 where λ and ε are positive parameters, ∆4u = div(|∇u| 2∇u), V is a continuous and periodic potential function with positive infimum, f(x, t) ∈ C(R3 × R, R) is p...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2023
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Schrödinger-Poisson rendszer - kvázilineáris, Differenciálegyenlet - parciális |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2023.1.48 |
| Online Access: | http://acta.bibl.u-szeged.hu/88791 |
| Tartalmi kivonat: | In this paper, we study the following quasilinear Schrödinger–Poisson system in R3 −∆u + V(x)u + λϕu = f(x, u), x ∈ R3 4∆4ϕ = λu 2 , x ∈ R3 where λ and ε are positive parameters, ∆4u = div(|∇u| 2∇u), V is a continuous and periodic potential function with positive infimum, f(x, t) ∈ C(R3 × R, R) is periodic with respect to x and only needs to satisfy some superquadratic growth conditions with respect to t. One nontrivial solution is obtained for λ small enough and ε fixed by a combination of variational methods and truncation technique. |
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| Terjedelem/Fizikai jellemzők: | 15 |
| ISSN: | 1417-3875 |