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arXiv · 2606.30522

A positive ground state for a planar Choquard equation with mixed diffusion and critical exponential growth

Shaoxiong Chen·Sekhar Ghosh·Vishvesh Kumar·Zhipeng Yang
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Abstract

We study a two-dimensional Choquard equation driven by the mixed local and nonlocal operator $L:=-\Delta+(-\Delta)^s$, where the nonlinearity has critical exponential growth of Trudinger--Moser type. Under a coercive assumption on the potential and suitable one-sided assumptions on the nonlinearity, we prove the existence of a least energy positive solution. The proof combines Nehari manifold minimization, compactness below the critical Trudinger--Moser threshold, local regularity, and a strong maximum principle.

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Shaoxiong Chen, Sekhar Ghosh, Vishvesh Kumar, Zhipeng Yang. 2026-06-29. A positive ground state for a planar Choquard equation with mixed diffusion and critical exponential growth. https://arxiv.org/abs/2606.30522

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