Nonlinear eigenvalue problems and bifurcation for quasi-linear elliptic operators

2020/11/10 by Emmanuel Wend Benedo Zongo, Zongo, Emmanuel Wend Benedo, Bernhard Ruf +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2011.05461

openalex publication_date 2020/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we analyze an eigenvalue problem for quasi-linear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We show that the eigenfunctions corresponding to the eigenvalues belong to L^∞, which implies C^1,α smoothness, and the first eigenvalue is simple. Moreover, we investigate the bifurcation results from trivial solutions using the Krasnoselski bifurcation theorem and from infinity using the Leray-Schauder degree. We also show the existence of multiple critical points using variational methods and the Krasnoselski genus.

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