Infinitely many solutions for nonhomogeneous Choquard equations
In this paper, we study the following nonhomogeneous Choquard equation −∆u + V(x)u = (Iα ∗ |u| p )|u| p−2u + f(x), x ∈ R N, where N ≥ 3, α ∈ (0, N), p ∈ N+α N N+α N−2 , Iα denotes the Riesz potential and f 6= 0. By using a critical point theorem for non-even functionals, we prove the existence of i...
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: | Choquard egyenlet, Differenciálegyenlet |
| doi: | 10.14232/ejqtde.2019.1.24 |
| Online Access: | http://acta.bibl.u-szeged.hu/58093 |
| Tartalmi kivonat: | In this paper, we study the following nonhomogeneous Choquard equation −∆u + V(x)u = (Iα ∗ |u| p )|u| p−2u + f(x), x ∈ R N, where N ≥ 3, α ∈ (0, N), p ∈ N+α N N+α N−2 , Iα denotes the Riesz potential and f 6= 0. By using a critical point theorem for non-even functionals, we prove the existence of infinitely many virtual critical points for two classes of potential V. To the best of our knowledge, this result seems to be the first one for nonhomogeneous Choquard equation on the existence of infinity many solutions. |
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| Terjedelem/Fizikai jellemzők: | 1-10 |
| ISSN: | 1417-3875 |