GENERALIZED EIGENVALUES OF THE (P, 2)-LAPLACIAN UNDER A PARAMETRIC BOUNDARY CONDITION

被引：9
|
作者：
Abreu, Jamil [1 ]
Madeira, Gustavo F. [2 ]
机构：
[1] Univ Fed Espirito Santo, Dept Matemat Aplicada, Rodovia BR 101,Km 60, Sao Mateus, ES, Brazil
[2] Univ Fed Sao Carlos UFSCar, Dept Matemat, Rod Washington Luis,Km 235, Sao Carlos, SP, Brazil
来源：
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2020年 / 63卷 / 01期
关键词：
eigenvalue problem; continuous family of eigenvalues; (p; 2)-Laplacian; Steklov boundary condition; boundary condition with eigenvalue parameter;
D O I：
10.1017/S0013091519000403
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study a general eigenvalue problem for the so called (p, 2)-Laplace operator on a smooth bounded domain Omega subset of R-N under a nonlinear Steklov type boundary condition, namely {-Delta(p)u - Delta u = lambda a(X)u in Omega, (vertical bar del u vertical bar(p-2) + 1)partial derivative u/partial derivative v = lambda b(x)u on partial derivative Omega. For positive weight functions a and b satisfying appropriate integrability and boundedness assumptions, we show that, for all p > 1, the eigenvalue set consists of an isolated null eigenvalue plus a continuous family of eigenvalues located away from zero.
引用
收藏
页码：287 / 303
页数：17
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