A class of degenerate elliptic eigenvalue problems

Advances in Nonlinear Analysis

article

Marcello Lucia¹  Friedemann Schuricht² 

[1] Mathematics Department, The City University of New York;Technische Universität Dresden

关键词: Nonlinear eigenvalue problems;    quasilinear elliptic equations;    critical point theory;    convex analysis;    nonsmooth analysis;   

DOI  :  10.1515/anona-2012-0202

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

Abstract. We consider a general class of eigenvalue problems where the leading elliptic term corresponds to a convex homogeneous energy function that is not necessarily differentiable. We derive a strong maximum principle and show uniqueness of the first eigenfunction. Moreover we prove the existence of a sequence of eigensolutions by using a critical point theory in metric spaces. Our results extend the eigenvalue problem of the p -Laplace operator to a much more general setting.

【 授权许可】

CC BY