Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201500348
Abstract: This paper studies the following nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents Δu+λ1up−1|x|s+μ1u2*(s1)−1|x|s1+αγ2*(s2)uα−1vβ|x|s2=0inΩ,Δv+λ2vp−1|x|s+μ2v2*(s1)−1|x|s1+βγ2*(s2)uαvβ−1|x|s2=0inΩ,u≥0,v≥0inΩ,u=0,v=0on∂Ω, where λ1,λ2,μ1,μ2,γ>0,2 1,α+β=2*(s2), Ω is a C1 open bounded domain in RN containing the origin, and N≥4. The existence result of positive… read more here.
Keywords: elliptic system; system involving; sobolev critical; hardy sobolev ... See more keywords
Positive Solutions for Elliptic Problems Involving Hardy–Sobolev–Maz’ya Terms
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Malaysian Mathematical Sciences Society"
DOI: 10.1007/s40840-018-0603-3
Abstract: In the present paper, we study the semilinear elliptic problem $$\displaystyle -\Delta u -\mu \frac{u}{|y|^{2}}=\frac{|u|^{2^{*}(s)-2}u}{|y|^{s}}+ f(x,u)$$-Δu-μu|y|2=|u|2∗(s)-2u|y|s+f(x,u) in bounded domain. Replacing the Ambrosetti–Rabinowitz condition by general superquadratic assumptions and the nonquadratic assumption, we establish the existence… read more here.
Keywords: problems involving; positive solutions; elliptic problems; hardy sobolev ... See more keywords
Extremals for Hardy-Sobolev type inequalities with monomial weights
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DOI: 10.1016/j.jmaa.2020.124645
Abstract: Abstract In this article we study the existence and non-existence of extremals for the following family of Hardy-Sobolev inequalities ( ∫ ( R + ) k × R N − k | x B u… read more here.
Keywords: extremals hardy; type inequalities; inequalities monomial; hardy sobolev ... See more keywords
Fractional Hardy-Sobolev operator with sign-changing and singular nonlinearity
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DOI: 10.1080/00036811.2019.1585535
Abstract: We study the following fractional equation with Hardy potential and singular nonlinearity where is a bounded domain in with smooth boundary , n>2s, , the sharp constant of the fractional Hardy Sobolev inequality, , with… read more here.
Keywords: sign changing; fractional hardy; hardy sobolev; singular nonlinearity ... See more keywords
Existence and Multiplicity of Nontrivial Solutions for Semilinear Elliptic Equations Involving Hardy-Sobolev Critical Exponents
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DOI: 10.3390/axioms13070450
Abstract: A class of semi-linear elliptic equations with the critical Hardy–Sobolev exponent has been considered. This model is widely used in hydrodynamics and glaciology, gas combustion in thermodynamics, quantum field theory, and statistical mechanics, as well… read more here.
Keywords: hardy sobolev; multiplicity nontrivial; existence multiplicity; elliptic equations ... See more keywords