Existence of solutions for Choquard equations with an $L^{1}$-integrable reciprocal potential and upper critical growth
Year: 2026
Type: article
Abstract: This paper is dedicated to studying the Choquard-type equation $$ \left \{ \textstyle\begin{array}{l} - \Delta u + V(x)u = ( {{I_{\alpha }} * {{\left | u \right |}^{ p}}} ){ \left | u \right |^{ p - 2}}u + \lambda {\left | u \right |^{q - 2}}u, \\ u \in H^{1} ({\mathbb{R}^{N}}), \end{array}\displaystyle \right . $$ { − Δ u + V ( x ) u = ( I α ∗ | u | p ) | u | p − 2 u + λ | u | q − 2 u , u ∈ H 1 ( R N ) , where $N\geq 3$ N ≥ 3 , $\alpha \in \left ({0,N}\right )$ α ∈ ( 0 , N ) , $1< q<2^{*}: = \frac{{2N}}{{N - 2}}$ 1 < q < 2 ∗ : = 2 N N − 2 (the critical Sobolev exponent), $p=\frac{N+\alpha }{N-2}$ p = N + α N − 2 is the upper critical Hardy-Littlewood-Sobolev exponent and $I_{\alpha }$ I α is the Riesz potential. When the reciprocal of the potential V is integrable, we establish the existence of solutions to the above problem for both sublinear and superlinear cases by means of the variational methods.
Source: Boundary Value Problems
Authors: Ting Guo, Tianle Xia, Xianhua Tang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,890
Awards: G8028717607, G8146664657
OpenAlex ID: W7138254306