The present paper is devoted to the quasilinear Choquard equation driven by the p-Laplacian operator (Formula presented) where 2 ≤ p < N, Iα denotes the Riesz potential of order α ∈ (0, N), and G ∈ C1(R, R). Assuming Berestycki–Lions type conditions on G, we prove the existence of a least energy solution u ∈ W1,p(RN) by means of variational methods. Moreover, we establish some qualitative properties of u when G is even and non–decreasing.
Existence of least energy solutions for a quasilinear Choquard equation / Ambrosio, V.; Autuori, G.; Isernia, T.. - In: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS. - ISSN 1534-0392. - 23:11(2024), pp. 1661-1678. [10.3934/cpaa.2024061]
Existence of least energy solutions for a quasilinear Choquard equation
Ambrosio V.;Autuori G.;Isernia T.
2024-01-01
Abstract
The present paper is devoted to the quasilinear Choquard equation driven by the p-Laplacian operator (Formula presented) where 2 ≤ p < N, Iα denotes the Riesz potential of order α ∈ (0, N), and G ∈ C1(R, R). Assuming Berestycki–Lions type conditions on G, we prove the existence of a least energy solution u ∈ W1,p(RN) by means of variational methods. Moreover, we establish some qualitative properties of u when G is even and non–decreasing.File | Dimensione | Formato | |
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