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
收藏
页码：372 / 387
页数：16
相关论文
共 50 条
  • [1] Parametric nonlinear singular Dirichlet problems
    Papageorgiou, Nikolaos S.
    Vetro, Calogero
    Vetro, Francesca
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 45 : 239 - 254
  • [2] EXACT BOUNDARY BEHAVIOR OF SOLUTIONS TO SINGULAR NONLINEAR DIRICHLET PROBLEMS
    Li, Bo
    Zhang, Zhijun
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2014,
  • [3] NONLINEAR DIRICHLET PROBLEMS WITH THE COMBINED EFFECTS OF SINGULAR AND CONVECTION TERMS
    Bai, Yunru
    Gasinski, Leszek
    Papageorgiou, Nikolaos S.
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2019,
  • [4] Some cases of weak continuity in nonlinear Dirichlet problems
    Boccardo, Lucio
    JOURNAL OF FUNCTIONAL ANALYSIS, 2019, 277 (10) : 3673 - 3687
  • [5] Parametric singular double phase Dirichlet problems
    Bai, Yunru
    Papageorgiou, Nikolaos S.
    Zeng, Shengda
    ADVANCES IN NONLINEAR ANALYSIS, 2023, 12 (01)
  • [6] Nonlinear nonhomogeneous singular problems
    Papageorgiou, Nikolaos S.
    Radulescu, Vicentiu D.
    Repovs, Dusan D.
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2020, 59 (01)
  • [7] Dirichlet problems with singular and superlinear terms
    Aizicovici, Sergiu
    Papageorgiou, Nikolaos S.
    Staicu, Vasile
    COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2015, 17 (06)
  • [8] ANISOTROPIC SINGULAR DOUBLE PHASE DIRICHLET PROBLEMS
    Papageorgiou, Nikolaos S.
    Radulescu, Vicentiu D.
    Zhang, Youpei
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2021, 14 (12): : 4465 - 4502
  • [9] Strong solutions for singular Dirichlet elliptic problems
    Godoy, Tomas
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022, (40) : 1 - 20
  • [10] Nonlinear nonhomogeneous Dirichlet problems with singular and convection terms
    Papageorgiou, Nikolaos S.
    Zhang, Youpei
    BOUNDARY VALUE PROBLEMS, 2020, 2020 (01)
12345