Multiple small solutions for Schrödinger equations involving the p-Laplacian and positive quasilinear term
We consider the multiplicity of solutions of a class of quasilinear Schrödinger equations involving the p-Laplacian: −∆pu + V(x)|u| p−2u + ∆p(u 2 )u = K(x)f(x, u), x ∈ R N, where ∆pu = div(|∇u| p−2∇u), 1 < p < N, N ≥ 3, V, K belong to C(RN) and f is an odd continuous function without any growt...
Elmentve itt :
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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 |
| Online Access: | http://acta.bibl.u-szeged.hu/69535 |
| Tartalmi kivonat: | We consider the multiplicity of solutions of a class of quasilinear Schrödinger equations involving the p-Laplacian: −∆pu + V(x)|u| p−2u + ∆p(u 2 )u = K(x)f(x, u), x ∈ R N, where ∆pu = div(|∇u| p−2∇u), 1 < p < N, N ≥ 3, V, K belong to C(RN) and f is an odd continuous function without any growth restrictions at large. Our method is based on a direct modification of the indefinite variational problem to a definite one. Even for the case p = 2, the approach also yields new multiplicity results. |
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| ISSN: | 1417-3875 |