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
Some new inequalities involving the Hardy operator
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DOI: 10.1002/mana.201900080
Abstract: In this paper we derive some new inequalities involving the Hardy operator, using some estimates of the Jensen functional, continuous form generalization of the Bellman inequality and a Banach spac ... read more here.
Keywords: inequalities involving; hardy operator; new inequalities; involving hardy ... 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