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math.AP2026

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

Shaoxiong Chen, Hichem Hajaiej, Min Yang +1

We study the Choquard equation involving mixed local and nonlocal operators \[ -Δu + (-Δ)^{s}u + V(x)u = \left(\frac{1}{|x|^μ} * F(u)\right) f(u) \quad \text{in } \mathbb{R}^{2}…

math.AP2026

Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators

Shaoxiong Chen, Min Yang, Zhipeng Yang

We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}Δu+\varepsilon^{2s}(-Δ)^{s}u+V(x)u=\varepsilon^{μ-2}\left(\frac{1}{|x|^μ}*F(u)\rig…