Two disjoint and infinite sets of solutions for an elliptic equation with critical Hardy-Sobolev-Maz'ya term and concave-convex nonlinearities

Rok, strany: 2023, 25 - 42

In this paper, we consider the following critical Hardy-Sobolev-Maz’ya problem $$ \left\{\begin{array}{ll} -\Delta u= \frac{\vert u\vert^{2^{*}(t)-2} u}{\vert y \vert^{t}} + \mu \vert u \vert ^{q-2} u & \; \text{in} \; \Omega, \\ u=0 & \; \text{on} \; \partial \Omega, \end{array}\right. $$ where $\Omega$ is an open bounded domain in $\mathbb{R}^{N}$, which contains some points $\left(0, z^{*}\right)$, $\mu > 0,$ $ 12\frac{q+1}{q-1}+t$, then the above problem has two disjoint and infinite sets of solutions. Here, we give a positive answer to one open problem proposed by Ambrosetti, Brezis and Cerami in \cite{AB} for the case of the critical Hardy-Sobolev-Maz’ya problem.

ISO 690:

Echarghaoui, R., Zaimi, Z. 2023. Two disjoint and infinite sets of solutions for an elliptic equation with critical Hardy-Sobolev-Maz'ya term and concave-convex nonlinearities. In Tatra Mountains Mathematical Publications, vol. 83, no.1, pp. 25-42. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0003

APA:

Echarghaoui, R., Zaimi, Z. (2023). Two disjoint and infinite sets of solutions for an elliptic equation with critical Hardy-Sobolev-Maz'ya term and concave-convex nonlinearities. Tatra Mountains Mathematical Publications, 83(1), 25-42. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0003

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

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