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.
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页码：372 / 387
页数：16
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