Ground states for a nonhomogeneous elliptic system involving Hardy–Sobolev critical exponents
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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
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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