Ground State Solutions for General Choquard Equation With the Riesz Fractional Laplacian

Sarah Abdullah Qadha, Muneera Abdullah Qadha, Haibo Chen and Yuying Zao

Advances in Mathematical Physics, 2025, vol. 2025, 1-13

Abstract: In this work, we study the existence of a nonzero solution for the following nonlinear general Choquard equation (CE): −Δν+ν=−ΔD−α2 ∗ Fνfν,in ℠N, where N≥3, F represents the primitive function of f,  f∈CR;R is a function that fulfils the general Berestycki–Lions conditions, ΔD denotes the Laplacian operator on Ω with zero Dirichlet boundary conditions and −ΔD−α2 is the Riesz fractional Laplacian of order α∈0,N. No prior research on the Riesz potential has been conducted in this specific context. The existence of this solution is demonstrated using variational approaches. This research is relevant and useful in many fields, particularly in mathematical analysis, theoretical physics, one-component plasma modelling, self-gravitating systems, nonlinear partial differential equations and quantum mechanics.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5974909

DOI: 10.1155/admp/5974909

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