@Article{Boccardo2026,
author = "Boccardo, Lucio and Tello, J. Ignacio and Tello, Lourdes",
title = "An elliptic system involving p-Laplacian and a chemotactic term",
journal = "Opuscula Math.",
year = "2026",
volume = "46",
number = "4",
pages = "491--511",
doi = "https://doi.org/10.7494/OpMath.OpMath.202607051",
url = "https://doi.org/10.7494/OpMath.OpMath.202607051",
abstract = "We study the nonlinear elliptic system: \[\begin{cases} u \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla u|^{p-2}\nabla u) + u = -\operatorname{div} (a(x) u|\nabla \psi|^{p-2}\nabla \psi) + f(x), \\ \psi \in W^{1,p}_0(\Omega): -\operatorname{div} (a(x)|\nabla \psi |^{p-2}\nabla \psi) = u^{\theta} \end{cases}\] in a bounded, open subset of \(\mathbb{R}^N\) for \(N \gt 2\) and \(2 \lt p \lt N\), where \(f\) satisfies: \[0 \leq f, \quad f\in L^{(p^*){'}}(\Omega), \quad p^*= \frac{Np}{N-p},\] \(a \in L^{\infty}(\Omega) \) is a given function such that there exist \(\alpha, \beta \in \mathbb{R}\) satisfying \[0\lt\alpha \leq a(x) \leq \beta, \quad x\in \Omega.\] We prove the existence of weak solutions in \([W^{1,p}_0(\Omega)]^2\) under the assumption \[0\lt \theta\lt 1- \frac{2}{p^*}.\]",
keywords = "nonlinear elliptic systems, weak solutions, \(p\)-Laplacian, chemotaxis term",
issn = "1232-9274"
}