Positive solutions for nonlinear Choquard equation with singular nonlinearity
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In this article, the existence and multiplicity of positive weak solutions of the Choquard equation with singular non-linearity was studied and the regularity of these weak solutions was studied.Abstract:
In this article, we study the following non-linear Choquard equation with singular non-linearitywhere is a bounded domain in with smooth boundary , and . Using variational approach and structure of associated Nehari manifold, we show the existence and multiplicity of positive weak solutions of the above problem, if is less than some positive constant. We also study the regularity of these weak solutions.read more
Citations
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References
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Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
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Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation
TL;DR: In this article, the Hartree-Fock theory of a plasma was used to prove existence and uniqueness of a minimization of the functional function of an electron trapped in its own hole.
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Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics
TL;DR: In this paper, the authors considered a semilinear elliptic problem and proved the existence of a positive groundstate solution of the Choquard or nonlinear Schr\"odinger--Newton equation for an optimal range of parameters.
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