Opuscula Math. 43, no. 4 (2023), 559-574
https://doi.org/10.7494/OpMath.2023.43.4.559

 
Opuscula Mathematica

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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  • 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
  • Communicated by Vicenţiu D. Rădulescu.
  • Received: 2023-01-30.
  • Revised: 2023-03-16.
  • Accepted: 2023-03-17.
  • Published online: 2023-06-13.
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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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