Localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth
Date
2022-02-10
Authors
Zhang, Bo
Liu, Xiangqing
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the existence of localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth -ɛp Δpv + V(x)|v|p-2v = ɛα-N |v|q-2v ∫ℝN |v(y)|q/ |x - y|α dy, x ∈ ℝN, where N ≥ 3, 1 < p < N, 0 < α < min{2p, N - 1}, p < q < p*α, p*α = p(2N - α)/ 2(N - p), V is a bounded function. By the perturbation method and the method of invariant sets of descending flow, for small ɛ we establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function V.
Description
Keywords
Quasilinear Choquard equation, Nodal solutions, Perturbation method
Citation
Zhang, B., & Liu, X. (2022). Localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth. <i>Electronic Journal of Differential Equations, 2022</i>(11), pp. 1-29.
Rights
Attribution 4.0 International