Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2502.03720 |
| Tags: |
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Sommario:
- We study the existence of least energy solutions for two Kirchhoff equations with the asymptotically cubic nonlinearity $f(u)=λu+η|u|^2u$ on a locally weighted and connected finite graph $G=(V,E)$. Such nonlinearity satisfies neither $\frac{F(u)}{u^4}\to +\infty$ as $|u|\to\infty$, where $F(u)=\int_0^uf(s)ds$, nor $\frac{f(u)}{u}\to 0$ as $u\to 0$. By utilizing the constrained variational method, we prove that there exist $λ_1\ge 0$ and $η_0\ge 0$ ($λ_1^*\ge 0$ and $η_0^*\ge 0$) such that these two equations have at least a least energy solution if $|λ|<aλ_1$ ($|λ|<aλ_1^*$) and $η>η_0$ ($η>η_0^*$).