Bifurcation from the first eigenvalue of the p-Laplacian with nonlinear boundary condition
Date
2019-02-21
Authors
Cuesta, Mabel
Leadi, Liamidi
Nshimirimana, Pascaline
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the problem
Δpu = |u|p-2u in Ω,
|∇u|p-2 ∂u/∂v = λ|u|p-2u + g(λ, x, u) on ∂Ω,
where Ω is a bounded domain of ℝN 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.
Description
Keywords
bifurcation theory, topological degree, p-Laplacian, elliptic problem, nonlinear boundary condition, maximum and anti-maximum principles
Citation
Cuesta, M., Leadi, L. A., & Nshimirimana, P. (2021). Bifurcation from the first eigenvalue of the p-Laplacian with nonlinear boundary condition. <i>Electronic Journal of Differential Equations, 2021</i>(32), pp. 1-29.
Rights
Attribution 4.0 International