Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912805168349184 |
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| author | Chen, Shaoxiong Yang, Min Yang, Zhipeng |
| author_facet | Chen, Shaoxiong Yang, Min Yang, Zhipeng |
| contents | We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}Δu+\varepsilon^{2s}(-Δ)^{s}u+V(x)u=\varepsilon^{μ-2}\left(\frac{1}{|x|^μ}*F(u)\right)f(u)\quad \text{in }\R^{2},\] where \(\varepsilon>0\), \(s\in(0,1)\), \(0<μ<2\), \(f\) has Trudinger--Moser critical exponential growth, and \(F(t)=\int_{0}^{t}f(τ)\,dτ\). By variational methods, combined with the Trudinger--Moser inequality and compactness arguments adapted to the critical growth and the nonlocal interaction term, we prove the existence of ground state solutions and describe their concentration behavior as \(\varepsilon\to0^{+}\). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03060 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators Chen, Shaoxiong Yang, Min Yang, Zhipeng Analysis of PDEs 35R11, 35B40, 35J20 We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}Δu+\varepsilon^{2s}(-Δ)^{s}u+V(x)u=\varepsilon^{μ-2}\left(\frac{1}{|x|^μ}*F(u)\right)f(u)\quad \text{in }\R^{2},\] where \(\varepsilon>0\), \(s\in(0,1)\), \(0<μ<2\), \(f\) has Trudinger--Moser critical exponential growth, and \(F(t)=\int_{0}^{t}f(τ)\,dτ\). By variational methods, combined with the Trudinger--Moser inequality and compactness arguments adapted to the critical growth and the nonlocal interaction term, we prove the existence of ground state solutions and describe their concentration behavior as \(\varepsilon\to0^{+}\). |
| title | Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators |
| topic | Analysis of PDEs 35R11, 35B40, 35J20 |
| url | https://arxiv.org/abs/2601.03060 |