Continuity results for parametric nonlinear singular Dirichlet problems

被引：12

作者：

Bai, Yunru ^{[1
]}

Motreanu, Dumitru ^{[2
]}

Zeng, Shengda ^{[1
]}

机构：

[1] Jagiellonian Univ Krakow, Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

[2] Univ Perpignan, Dept Math, F-66860 Perpignan, France

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2020年 / 9卷 / 01期

基金：

欧盟地平线“2020”;

关键词：

Parametric singular elliptic equation; p-Laplacian; smallest solution; sequential continuity; monotonicity; MULTIPLE CONSTANT SIGN; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; NODAL SOLUTIONS; BIFURCATION; CONVECTION; EXISTENCE;

D O I：

10.1515/anona-2020-0005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study from a qualitative point of view the nonlinear singular Dirichlet problem depending on a parameter lambda > 0 that was considered in [32]. Denoting by S-lambda the set of positive solutions of the problem corresponding to the parameter lambda, we establish the following essential properties of S lambda: (i) there exists a smallest element u(lambda)* in S-lambda, and the mapping lambda -> u(lambda)* is (strictly) increasing and left continuous; (ii) the set-valued mapping lambda -> S-lambda is sequentially continuous.

引用

页码：372 / 387

页数：16

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