Choquard equations with mixed potential

Romildo N. Lima () and Marco A. S. Souto ()
Additional contact information
Romildo N. Lima: Universidade Federal de Campina Grande
Marco A. S. Souto: Universidade Federal de Campina Grande

Partial Differential Equations and Applications, 2023, vol. 4, issue 4, 1-18

Abstract: Abstract In this paper, we study the following class of nonlinear Choquard equation, $$\begin{aligned} -\Delta u+a(z)u=K(u)f(u)\quad \text {in}\quad \mathbb {R}^N, \end{aligned}$$ - Δ u + a ( z ) u = K ( u ) f ( u ) in R N , where $$\mathbb {R}^N=\mathbb {R}^L\times \mathbb {R}^M$$ R N = R L × R M , $$L\ge 2$$ L ≥ 2 , $$K(u)=|.|^{-\gamma }*F(u)$$ K ( u ) = | . | - γ ∗ F ( u ) , $$\gamma \in (0,N)$$ γ ∈ ( 0 , N ) , a is a continuous real function and F is the primitive function of f. Under some suitable assumptions mixed on the potential a. We prove existence of a nontrivial solution for the above equation.

Keywords: Nonlinear Choquard equation; Nonlocal nonlinearities; Mixed potential; Variational methods; 35J50; 35J60; 35A15 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s42985-023-00253-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00253-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-023-00253-z

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().