BIFURCATION FROM THE FIRST EIGENVALUE OF THE p-LAPLACIAN WITH NONLINEAR BOUNDARY CONDITION - Archive ouverte HAL Access content directly
Journal Articles Electronic Journal of Differential Equations Year : 2019

BIFURCATION FROM THE FIRST EIGENVALUE OF THE p-LAPLACIAN WITH NONLINEAR BOUNDARY CONDITION

Abstract

We consider the problem ∆pu = |u| p−2 u in Ω, |∇u| p−2 ∂u ∂ν = λ|u| p−2 u + g(λ, x, u) on ∂Ω, where Ω is a bounded domain of R N with smooth boundary, N ≥ 2, and ∆p denotes the p-Laplacian operator. We give sufficient conditions for the existence of continua of solutions bifurcating from both zero and infinity at the principal eigenvalue of p-Laplacian with nonlinear boundary conditions. We also prove that those continua split on two, one containing strictly positive and the other containing strictly negative solutions. As an application we deduce results on anti-maximum and maximum principles for the p-Laplacian operator with nonlinear boundary conditions.
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Dates and versions

hal-04121214 , version 1 (07-06-2023)

Identifiers

  • HAL Id : hal-04121214 , version 1

Cite

Mabel Cuesta, Liamidi A Leadi, Pascaline Nshimirimana. BIFURCATION FROM THE FIRST EIGENVALUE OF THE p-LAPLACIAN WITH NONLINEAR BOUNDARY CONDITION. Electronic Journal of Differential Equations, 2019, 2019 (32), pp.1-11. ⟨hal-04121214⟩
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