Remarks on the non-local eigenvalue problems for the p-Laplacian

被引：0
|
作者：
Tanaka, Mieko [1 ]
机构：
[1] Tokyo Univ Sci, Dept Math, Kagurazaka 1-3,Shinjuku Ku, Tokyo 1628601, Japan
来源：
BOUNDARY VALUE PROBLEMS | 2025年 / 2025卷 / 01期
基金：
日本学术振兴会;
关键词：
Sobolev-Poincare inequality; p-Laplacian; Nonlinear eigenvalue with weight; Second eigenvalue of the p-Laplacian; Nodal eigen function; ELLIPTIC-EQUATIONS; EIGENFUNCTIONS; ASYMPTOTICS; CONSTANTS;
D O I：
10.1186/s13661-025-02016-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the p-Laplace eigenvalue problem -Delta(p)u =lambda w(x) u lu in 2. u=0 on partial derivative Omega. having a nonlocal term [u(q)Omega integral(q,w)a w/u/9dx > 0. The first eigenvalue is well known as the best constant of the Sobolev-Poicar & eacute; inequality. In this paper, we give the existence of the least eigenvalue mu" such that the equation has a nodal solution, We show that u coincides with the second eigenvalue in p-sublinear case (1 <q<p) provided w >= 0 a.e. in 2. In p-superlinear case (p <q<p(2)), we characterize " by the minimax value using the Rayleigh quotient.
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页数：19
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