Positive solutions for nonlinear Choquard equation with singular nonlinearity
TLDR
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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Multiple positive solutions for critical elliptic problem with singularity
Shengbin Yu,Jianqing Chen +1 more
TL;DR: In this paper, the authors investigated the critical elliptic problem with singularity and established a relation between the number of maxima of Q(x) and positive solutions by variational method and Nehari type constraint.
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Critical Kirchhoff-Choquard system involving the fractional $p$-Laplacian operator and singular nonlinearities
TL;DR: In this article, a class of critical fractional $p$-Laplacian Kirchhoff-Choquard systems with singular nonlinearities and two parameters was studied, and the existence of two positive solutions for above systems when $\lambda$ and $\mu$ satisfy suitable conditions.
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Ground States Solutions for a Modified Fractional Schrödinger Equation with a Generalized Choquard Nonlinearity
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Fractional schrödinger–poisson system with singularity: existence, uniqueness, and asymptotic behavior
Shengbin Yu,Jianqing Chen +1 more
TL;DR: In this paper, the existence, uniqueness, and monotonicity of positive solution uλ using the variational method were shown for fractional Schrodinger-Poisson systems with singularity under certain assumptions on V and f.
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