@Article{Alreshidi2024,
author = "Alreshidi, B. and Hai, D.D.",
title = "Uniqueness for a class p-Laplacian problems when a parameter is large",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "1",
pages = "5--17",
doi = "https://doi.org/10.7494/OpMath.2024.44.1.5",
url = "https://doi.org/10.7494/OpMath.2024.44.1.5",
abstract = "We prove uniqueness of positive solutions for the problem \[-\Delta_{p}u=\lambda f(u)\text{ in }\Omega,\ u=0\text{ on }\partial \Omega,\] where \(1\lt p\lt 2\) and \(p\) is close to 2, \(\Omega\) is bounded domain in \(\mathbb{R}^{n}\) with smooth boundary \(\partial \Omega\), \(f:[0,\infty)\rightarrow [0,\infty )\) with \(f(z)\sim z^{\beta }\) at \(\infty\) for some \(\beta \in (0,1)\), and \(\lambda\) is a large parameter. The monotonicity assumption on \(f\) is not required even for \(u\) large.",
keywords = "singular \(p\)-Laplacian, uniqueness, positive solutions",
issn = "1232-9274"
}