Infinitely many solutions to quasilinear Schrödinger equations with critical exponent
This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: −∆pu + V(x)|u| p−2u − ∆p(|u| 2ω)|u| 2ω−2u = ak(x)|u| q−2u + b|u| 2ωp ∗−2u, x ∈ R N. Here ∆pu = div(|∇u| p−2∇u) is the p-Laplacian operator with 1 < p < N, p N p N−p is the critical Sobolev expo...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2019
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Schrödinger egyenlet |
| doi: | 10.14232/ejqtde.2019.1.5 |
| Online Access: | http://acta.bibl.u-szeged.hu/58112 |
| Tartalmi kivonat: | This paper is concerned with the following quasilinear Schrödinger equations with critical exponent: −∆pu + V(x)|u| p−2u − ∆p(|u| 2ω)|u| 2ω−2u = ak(x)|u| q−2u + b|u| 2ωp ∗−2u, x ∈ R N. Here ∆pu = div(|∇u| p−2∇u) is the p-Laplacian operator with 1 < p < N, p N p N−p is the critical Sobolev exponent. 1 ≤ 2ω < q < 2ωp, a and b are suitable positive parameters, V ∈ C(RN, [0, ∞)), k ∈ C(RN, R). With the help of the concentration-compactness principle and R. Kajikiya’s new version of symmetric Mountain Pass Lemma, we obtain infinitely many solutions which tend to zero under mild assumptions on V and k. |
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| Terjedelem/Fizikai jellemzők: | 1-16 |
| ISSN: | 1417-3875 |