Schrödinger‐Poisson system with Hardy‐Littlewood‐Sobolev critical exponent
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5694
Abstract: In this paper, we consider the following Schrödinger‐Poisson system: −Δu+λϕ|u|2α∗−2u=∫R3|u|2β∗|x−y|3−βdy|u|2β∗−2u,inR3,(−Δ)α2ϕ=Aα−1|u|2α∗,inR3, where parameters α,β∈(0,3),λ>0, Aα=Γ(3−α2)2απ32Γ(α2) , 2α∗=3+α , and 2β∗=3+β are the Hardy‐Littlewood‐Sobolev critical exponents. For α0, we prove the existence of nonnegative groundstate solution to… read more here.
Keywords: dinger poisson; system; hardy littlewood; littlewood sobolev ... See more keywords
Hardy—Littlewood—Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs
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DOI: 10.1007/s10114-019-8417-2
Abstract: The purpose of this paper is five-fold. First, we employ the harmonic analysis techniques to establish the following Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel on the upper half space $$\int_{\mathbb{R}_ + ^n} {{{\int_{\partial \mathbb{R}_… read more here.
Keywords: fractional poisson; hardy littlewood; mathbb; littlewood sobolev ... See more keywords
Multiplicity Results for Kirchhoff Equations with Hardy-Littlewood-Sobolev Critical Nonlinearity
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DOI: 10.1007/s10883-019-09456-3
Abstract: In this paper, we deal with the multiplicity results for Kirchhoff equations with Hardy-Littlewood-Sobolev critical nonlinearity in ℝ N $\mathbb {R}^{N}$ . By using the second concentration-compactness principle and concentration-compactness principle at infinity to prove… read more here.
Keywords: equations hardy; hardy littlewood; littlewood sobolev; results kirchhoff ... See more keywords