Positive ground state of coupled planar systems of nonlinear Schrödinger equations with critical exponential growth
In this paper, we prove the existence of a positive ground state solution to the following coupled system involving nonlinear Schrödinger equations: −∆u + V1(x)u = f1(x, u) + λ(x)v, x ∈ R2 −∆v + V2(x)v = f2(x, v) + λ(x)u, x ∈ R2 where λ, V1, V2 ∈ C(R2 ,(0, +∞)) and f1, f2 : R2 × R → R have critical...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Schrödinger egyenlet, Trudinger-Moser-egyenlőtlenség |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.48 |
| Online Access: | http://acta.bibl.u-szeged.hu/78333 |
| Tartalmi kivonat: | In this paper, we prove the existence of a positive ground state solution to the following coupled system involving nonlinear Schrödinger equations: −∆u + V1(x)u = f1(x, u) + λ(x)v, x ∈ R2 −∆v + V2(x)v = f2(x, v) + λ(x)u, x ∈ R2 where λ, V1, V2 ∈ C(R2 ,(0, +∞)) and f1, f2 : R2 × R → R have critical exponential growth in the sense of Trudinger–Moser inequality. The potentials V1(x) and V2(x) satisfy a condition involving the coupling term λ(x), namely 0 < λ(x) ≤ λ0 p V1(x)V2(x). We use non-Nehari manifold, Lions’s concentration compactness and strong maximum principle to get a positive ground state solution. Moreover, by using a bootstrap regularity lifting argument and L q -estimates we get regularity and asymptotic behavior. Our results improve and extend the previous results. |
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| ISSN: | 1417-3875 |