# Multiplicity of solutions for homogeneous elliptic systems with critical growth - Mathematics > Analysis of PDEs

Multiplicity of solutions for homogeneous elliptic systems with critical growth - Mathematics > Analysis of PDEs - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: In this paper we are concerned with the number of nonnegative solutions ofthe elliptic system $${array}{ll} -\Delta u = Q uu,v + 1-2{2^*} H uu,v,and{in} \Omega,\vdois\ -\Delta v = Q vu,v + 1-{2^*} H vu,v,and {in}\Omega,\vdois\ u=v=0,and {on} \partial\Omega. \leqno{P}$$ where $\Omega\subset \mathbb{R}^N$ is a bounded smooth domain, $N \geq 3$, $2^*:=2N-N-2$and $Q u, H u$ and $Q v$, $H v$ are the partial derivatives of the homogeneousfunctions $Q,\,H \in C^1\mathbb{R}^2 +,\mathbb{R}$, where $\mathbb{R}^2 + :=0,\infty \times 0,\infty$. In the proofs we apply variational methods andLjusternik-Schnirelmann theory.

Autor: Marcelo F. Furtado, João Pablo P. Silva

Fuente: https://arxiv.org/