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- W2952354120 abstract "We consider the following Kirchhoff - Choquard equation [ -M(|na u|_{L^2}^{2})De u = la f(x)|u|^{q-2}u+ left(int_{Om}frac{|u(y)|^{2^*_{mu}}}{|x-y|^{mu}}dyright)|u|^{2^*_{mu}-2}u ; text{in}; Om,quad u = 0 ; text{ on } pa Om , ] where $Om$ is a bounded domain in $mathbb{R}^N( Ngeq 3)$ with $C^2$ boundary, $2^*_{mu}=frac{2N-mu}{N-2}$, $1<qleq 2$, and $f$ is a continuous real valued sign changing function. When $1<q< 2$, using the method of Nehari manifold and Concentration-compactness Lemma, we prove the existence and multiplicity of positive solutions of the above problem. We also prove the existence of a positive solution when $q=2$ using the Mountain Pass Lemma." @default.
- W2952354120 created "2019-06-27" @default.
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- W2952354120 date "2019-01-31" @default.
- W2952354120 modified "2023-10-14" @default.
- W2952354120 title "Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity" @default.
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- W2952354120 doi "https://doi.org/10.48550/arxiv.1901.11310" @default.
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