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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2408.16364 |
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- We investigate the existence and multiplicity of solutions for a class of generalized coupled system involving poly-Laplacian and a parameter $λ$ on finite graphs. By using mountain pass lemma together with cut-off technique, we obtain that system has at least a nontrivial weak solution $(u_λ,v_λ)$ for every large parameter $λ$ when the nonlinear term $F(x,u,v)$ satisfies superlinear growth conditions only in a neighborhood of origin point $(0,0)$. We also obtain a concrete form for the lower bound of parameter $λ$ and the trend of $(u_λ,v_λ)$ with the change of parameter $λ$. Moreover, by using a revised Clark's theorem together with cut-off technique, we obtain that system has a sequence of solutions tending to 0 for every $λ>0$ when the nonlinear term $F(x,u,v)$ satisfies sublinear growth conditions only in a neighborhood of origin point $(0,0)$.