Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2408.00654 |
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Sommario:
- In this paper, we study the following class of weighted Choquard equations \begin{align*} -Δu =λu + \Bigg(\displaystyle\int\limits_Ω\frac{Q(|y|)F(u(y))}{|x-y|^μ}dy\Bigg) Q(|x|)f(u) ~~\textrm{in}~~ Ω~~ \text{and}~~ u=0~~ \textrm{on}~~ \partial Ω, \end{align*} where $Ω\subset \mathbb{R}^2$ is a bounded domain with smooth boundary, $μ\in (0,2)$ and $λ>0$ is a parameter. We assume that $f$ is a real valued continuous function satisfying critical exponential growth in the Trudinger-Moser sense, and $F$ is the primitive of $f$. Let $Q$ be a positive real valued continuous weight, which can be singular at zero. Our main goal is to prove the existence of a nontrivial solution for all parameter values except the resonant case, i.e., when $λ$ coincides with any of the eigenvalues of the operator $(-Δ, H^1_0(Ω))$.