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Continuity results for parametric nonlinear singular Dirichlet problems
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DOI：10.1515/anona-2020-0005.png)
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摘要
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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.
Keyword:
Parametric singular elliptic equation
p-Laplacian
smallest solution
sequential continuity
monotonicity
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论文数:
678
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1.4K
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