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arXiv · 2603.23870

Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators

Shaoxiong Chen·Hichem Hajaiej·Min Yang·Zhipeng Yang
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Abstract

We study the Choquard equation involving mixed local and nonlocal operators \[ -\Delta u + (-\Delta)^{s}u + V(x)u = \left(\frac{1}{|x|^{\mu}} * F(u)\right) f(u) \quad \text{in } \mathbb{R}^{2}, \] where $s\in(0,1)$, $\mu\in(0,2)$, $F(t)=\int_{0}^{t} f(\tau)\,d\tau$, and $f$ has subcritical exponential growth of Trudinger--Moser type. Under suitable assumptions on the potential $V$ and the nonlinearity $f$, we prove the existence of a least energy positive solution by a Nehari manifold approach. We also establish the existence of a sign-changing solution by means of invariant sets of descending flow. If, in addition, the nonlinearity is odd, then the problem admits infinitely many sign-changing solutions.

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Shaoxiong Chen, Hichem Hajaiej, Min Yang, Zhipeng Yang. 2026-03-25. Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators. https://doi.org/10.1007/s11868-026-00802-1

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