In this paper, by an approximating argument, we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents $ \left\{\begin{array}{ll} -\Delta u=\mu \vert u \vert ^{2^{*}-2} u +\frac{ \vert u \vert ^{2^{*}(s)-2}u}{ \vert x \vert ^{s}}+ a(x) \vert u \vert ^{q-2} u & \;{\rm in} \; \Omega, \\ u=0 & \;{\rm on} \; \partial \Omega, \end{array}\right.$ where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$ with $0\in \partial \Omega$ and all the principle curvatures of $ \partial \Omega$ at 0 are negative, $a \in \mathcal{C}^{1}(\bar{\Omega}, \mathbb{R^{\ast}}^{+}), $ $ \mu> 0, $ $0<s<2, $ $1<q<2$ and $N > 2\frac{q+1}{q -1}.$ By $2^{*}:=\frac{2 N}{N-2}$ and $2^{*}(s):=\frac{2 (N-s)}{N-2}$ we denote the critical Sobolev exponent and Hardy-Sobolev exponent, respectively.
Khalid BOUABID
,
Rachid ECHARGHAOUI
,
Mohssine EL MANSOUR
. TWO DISJOINT AND INFINITE SETS OF SOLUTIONS FOR AN ELLIPTIC EQUATION INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS*[J]. Acta mathematica scientia, Series B, 2023
, 43(5)
: 2061
-2074
.
DOI: 10.1007/s10473-023-0508-6
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