Opuscula Mathematica
Opuscula Math. 43, no. 4 (2023), 559-574

The first eigencurve for a Neumann boundary problem involving p-Laplacian with essentially bounded weights

Ahmed Sanhaji
Ahmed Dakkak
Mimoun Moussaoui
Abstract. This article is intended to prove the existence and uniqueness of the first eigencurve, for a homogeneous Neumann problem with singular weights associated with the equation \[-\Delta_{p} u=\alpha m_{1}|u|^{p-2}u+\beta m_{2}|u|^{p-2}u\] in a bounded domain \(\Omega \subset \mathbb{R}^{N}\). We then establish many properties of this eigencurve, particularly the continuity, variational characterization, asymptotic behavior, concavity and the differentiability.
Keywords: \(p\)-Laplacian, first eigencurve, singular weight, Neumann boundary conditions.
Mathematics Subject Classification: 35J30, 35J60, 35J66.
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About the authors ▼
Ahmed Sanhaji (corresponding author)
Sidi Mohamed Ben Abdellah University, Polydisciplinary Faculty of Taza, Department of Mathematics, LSI Laboratory, P.O. Box 1223 Taza, 35000, Morocco
Ahmed Dakkak
Sidi Mohamed Ben Abdellah University, Polydisciplinary Faculty of Taza, Department of Mathematics, LSI Laboratory, P.O. Box 1223 Taza, 35000, Morocco
Mimoun Moussaoui
Mohamed 1 University, Faculty of Sciences of Oujda, Department of Mathematics, LANOL Laboratory, P.O. Box 717 Oujda, 60000, Morocco
About the article ▼
Communicated by Vicenţiu D. Rădulescu.
Received: 2023-01-30.
Revised: 2023-03-16.
Accepted: 2023-03-17.
Published online: 2023-06-13.
Cite this article as ▼
Ahmed Sanhaji, Ahmed Dakkak, Mimoun Moussaoui, The first eigencurve for a Neumann boundary problem involving p-Laplacian with essentially bounded weights, Opuscula Math. 43, no. 4 (2023), 559-574, https://doi.org/10.7494/OpMath.2023.43.4.559.
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