The Dirichlet problem for the 1-Laplacian with a general singular term and L <sup>1</sup>-data

نویسندگان

چکیده

We study the Dirichlet problem for an elliptic equation involving $1$-Laplace operator and a reaction term, namely: $$ \left\{\begin{array}{ll} \displaystyle -\Delta_1 u =h(u)f(x)&\hbox{in }\Omega\,,\\ u=0&\hbox{on }\partial\Omega\,, \end{array}\right. where $ \Omega \subset \mathbb{R}^N$ is open bounded set having Lipschitz boundary, $f\in L^1(\Omega)$ nonnegative, $h$ continuous real function that may possibly blow up at zero. investigate optimal ranges data in order to obtain existence, nonexistence (whenever expected) uniqueness of nonnegative solutions.

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ژورنال

عنوان ژورنال: Nonlinearity

سال: 2021

ISSN: ['0951-7715', '1361-6544']

DOI: https://doi.org/10.1088/1361-6544/abc65b