Fractional logarithmic Schrödinger equations on lattice graphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909317265883136 |
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| author | Wang, Lidan |
| author_facet | Wang, Lidan |
| contents | In this paper, we study the fractional logarithmic Schrödinger equation $$ (-Δ)^{s} u+h(x) u=u \log u^{2} $$ on lattice graphs $\mathbb{Z}^d$, where $s\in (0,1)$. If $h(x)$ is a bounded periodic potential, we prove the existence of ground state solution by mountain pass theorem and Lions lemma. If $h(x)$ is a coercive potential, we show the existence of ground state sign-changing solutions by the method of Nehari manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09976 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional logarithmic Schrödinger equations on lattice graphs Wang, Lidan Analysis of PDEs 35A15, 35R11, 35R02 In this paper, we study the fractional logarithmic Schrödinger equation $$ (-Δ)^{s} u+h(x) u=u \log u^{2} $$ on lattice graphs $\mathbb{Z}^d$, where $s\in (0,1)$. If $h(x)$ is a bounded periodic potential, we prove the existence of ground state solution by mountain pass theorem and Lions lemma. If $h(x)$ is a coercive potential, we show the existence of ground state sign-changing solutions by the method of Nehari manifold. |
| title | Fractional logarithmic Schrödinger equations on lattice graphs |
| topic | Analysis of PDEs 35A15, 35R11, 35R02 |
| url | https://arxiv.org/abs/2409.09976 |