Existence of Solutions for Planar Kirchhoff–Choquard Problems

Rui Niu and Tianxing Wu ()
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Rui Niu: College of Science, Heilongjiang Institute of Technology, Harbin 150050, China
Tianxing Wu: No. 703 Research Institute, China State Shipbuilding Co., Ltd., Harbin 150078, China

Mathematics, 2023, vol. 11, issue 17, 1-19

Abstract: In this article, we are interested in the study of the following Kirchhoff–Choquard equations: − a + b ∫ R 2 | ∇ u | 2 d x Δ u + V ( x ) u = λ ( ln | x | ∗ u 2 ) u + f ( u ) , x ∈ R 2 , where λ > 0 , a > 0 , b > 0 , V and f are continuous functions with some appropriate assumptions. We prove that when the parameter λ is sufficiently small, the above problem has a mountain pass solution, a least energy solution and a ground state solution by applying the variational methods and building some subtle inequalities.

Keywords: Choquard problem; Kirchhoff-type problems; variational methods; mountain pass solution; ground state solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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