Existence of multiple positive weak solutions and estimates for extremal values for a class of concave-convex elliptic problems with an inverse-square potential
Yaoping Chen Jianqing Chen
Communications on Pure & Applied Analysis 2017, 16(5): 1531-1552 doi: 10.3934/cpaa.2017073
In this paper, variational methods are used to establish some existence and multiplicity results and provide uniform estimates of extremal values for a class of elliptic equations of the form:
$-Δ u - {{λ}\over{|x|^2}}u = h(x) u^q + μ W(x) u^p,\ \ x∈Ω\backslash\{0\}$
with Dirichlet boundary conditions, where
$0∈ Ω\subset\mathbb{R}^N $
$N≥q 3 $
) be a bounded domain with smooth boundary
$\partial Ω $
$μ>0 $
is a parameter,
$0 < λ < Λ={{(N-2)^2}\over{4}}$, $0 < q < 1 < p < 2^*-1 $
$h(x)>0 $
$W(x) $
is a given function with the set
$\{x∈ Ω: W(x)>0\} $
of positive measure.
keywords: Elliptic problems Hardy term multiple positive solutions extremal values uniform estimates

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