On the eigenvalue problem involving the weighted p-Laplacian in radially symmetric domains

被引：3

作者：

Drabek, Pavel ^{[1
]}

Ho, Ky ^{[2
]}

Sarkar, Abhishek ^{[3
]}

机构：

[1] Univ West Bohemia, Dept Math, Univ 8, Plzen 30614, Czech Republic

[2] Duy Tan Univ, Inst Fundamental & Appl Sci, Ho Chi Minh City 700000, Vietnam

[3] Univ West Bohemia, NTIS, Tech 8, Plzen 30614, Czech Republic

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 468卷 / 02期

关键词：

The weighted p-Laplacian; The first eigenvalue; Exterior domain; Regularity; Asymptotic behavior; Maximum principles; Variational method; DEGENERATE ELLIPTIC-EQUATIONS; STURM-LIOUVILLE PROBLEM; UNBOUNDED-DOMAINS; REGULARITY; PRINCIPLE;

D O I：

10.1016/j.jmaa.2018.08.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the following eigenvalue problem {-div (L(x) vertical bar del u vertical bar(p-2)del u) = lambda K(x)vertical bar u vertical bar(p-2)u in A(R1)(R2), u = 0 on partial derivative A(R1)(R2), where A(R1)(R2) := {x is an element of R-N : R1 < vertical bar x vertical bar < R-2} (0 < R-1 < R-2 <= infinity), lambda > 0 is a parameter, the weights L and K are measurable with L positive a.e. in A(R1)(R2) and K possibly sign-changing in A(R1)(R2). We prove the existence of the first eigenpair and discuss the regularity and positiveness of eigenfunctions. The asymptotic estimates for u(x) and del u(x) as vertical bar x vertical bar -> R-1(+) or R-2(-) are also investigated. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：716 / 756

页数：41

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