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Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity
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In this paper we prove the existence and uniqueness of positive classical solution of the fractional Laplacian with singular nonlinearity in a smooth bounded domain with zero Drichlet boundary conditions. By the method of sub-supersolution, we derive the existence of positive classical solution to the approximation problems. In order to obtain the regularity, we first establish the existence of weak solution for the fraction Laplacian. Thanks to \cite{XY}, the regularity follows from the boundedness of weak solution.
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Cited by 2 Pith papers
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Existence Theory for a class of semilinear mixed local and nonlocal equations involving variable singularities and singular measures
Existence of weak solutions is proven for mixed local-nonlocal singular elliptic problems with variable singular exponents and singular measure-valued data.
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Regularity and existence for semilinear mixed local-nonlocal equations with variable singularities and measure data
Existence and regularity are established for semilinear mixed local-nonlocal problems with variable singular exponent and measure-valued data, including the case of two simultaneous measure sources.
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