Opuscula Mathematica
Opuscula Math. 44, no. 1 (2024), 5-17

Uniqueness for a class p-Laplacian problems when a parameter is large

B. Alreshidi
D.D. Hai
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.
Mathematics Subject Classification: 35J92, 35J75.
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About the authors ▼
B. Alreshidi
Mississippi State University, Department of Mathematics and Statistics, Mississippi State, MS 39762, USA
D.D. Hai (corresponding author)
Mississippi State University, Department of Mathematics and Statistics, Mississippi State, MS 39762, USA
About the article ▼
Communicated by Vicenţiu D. Rădulescu.
Received: 2023-02-22.
Revised: 2023-08-23.
Accepted: 2023-08-27.
Published online: 2023-10-27.
Cite this article as ▼
B. Alreshidi, D.D. Hai, Uniqueness for a class p-Laplacian problems when a parameter is large, Opuscula Math. 44, no. 1 (2024), 5-17, https://doi.org/10.7494/OpMath.2024.44.1.5.
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