Existence of weak solutions for quasilinear Schrödinger equations with a parameter
In this paper, we study the following quasilinear Schrödinger equation of the form −∆pu + V(x)|u| p−2u − h ∆p(1 + u 2 α/2i αu 2(1 + u 2) (2−α)/2 = k(u), x ∈ R N, where p-Laplace operator ∆pu = div(|∇u| p−2∇u) (1 < p ≤ N) and α ≥ 1 is a parameter. Under some appropriate assumptions on the potentia...
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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: | Schrödinger egyenlet, Differenciálegyenlet, Laplace-operátor |
| doi: | 10.14232/ejqtde.2020.1.41 |
| Online Access: | http://acta.bibl.u-szeged.hu/70154 |
| LEADER | 01420nas a2200229 i 4500 | ||
|---|---|---|---|
| 001 | acta70154 | ||
| 005 | 20211020135208.0 | ||
| 008 | 201201s2020 hu o 0|| zxx d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2020.1.41 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Wei Yunfeng | |
| 245 | 1 | 0 | |a Existence of weak solutions for quasilinear Schrödinger equations with a parameter |h [elektronikus dokumentum] / |c Wei Yunfeng |
| 260 | |c 2020 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a In this paper, we study the following quasilinear Schrödinger equation of the form −∆pu + V(x)|u| p−2u − h ∆p(1 + u 2 α/2i αu 2(1 + u 2) (2−α)/2 = k(u), x ∈ R N, where p-Laplace operator ∆pu = div(|∇u| p−2∇u) (1 < p ≤ N) and α ≥ 1 is a parameter. Under some appropriate assumptions on the potential V and the nonlinear term k, using some special techniques, we establish the existence of a nontrivial solution in C 1,β loc (RN) (0 < β < 1), we also show that the solution is in L ∞(RN) and decays to zero at infinity when 1 < p < N. | |
| 695 | |a Schrödinger egyenlet, Differenciálegyenlet, Laplace-operátor | ||
| 700 | 0 | 1 | |a Chen Caisheng |e aut |
| 700 | 0 | 1 | |a Yang Hongwei |e aut |
| 700 | 0 | 1 | |a Yu Hongwang |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/70154/1/ejqtde_2020_041.pdf |z Dokumentum-elérés |