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

Sanhaji Ahmed, Dakkak Ahmed, Moussaoui Mimoun

Opuscula Mathematica

2023

Vol. 43, no. 4

559--574

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 −Δp u = αm1|u|p−2u + βm2|u|p−2u in a bounded domain Ω ⊂ RN. We then establish many properties of this eigencurve, particularly the continuity, variational characterization, asymptotic behavior, concavity and the differentiability.