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...
Elmentve itt :
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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 |
| LEADER | 01692nas a2200229 i 4500 | ||
|---|---|---|---|
| 001 | acta78333 | ||
| 005 | 20230313102906.0 | ||
| 008 | 230313s2022 hu o 0|| eng d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2022.1.48 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Chen Jing | |
| 245 | 1 | 0 | |a Positive ground state of coupled planar systems of nonlinear Schrödinger equations with critical exponential growth |h [elektronikus dokumentum] / |c Chen Jing |
| 260 | |c 2022 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a 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. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Schrödinger egyenlet, Trudinger-Moser-egyenlőtlenség | ||
| 700 | 0 | 1 | |a Zhang Xinghua |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/78333/1/ejqtde_2022_048.pdf |z Dokumentum-elérés |