Existence and symmetry results for competing variational systems

Details Existence and symmetry results for competing variational systems Existence and symmetry results for competing variational systems

2012-01-25

arxiv.org/abs/1201.5206v1

Mathematics

Analysis of PDEs

21 pages, 0 figures

Scientific paper

In this paper we consider a class of gradient systems of type $$ -c_i \Delta u_i + V_i(x)u_i=P_{u_i}(u),\quad u_1,..., u_k>0 \text{in}\Omega, \qquad u_1=...=u_k=0 \text{on} \partial \Omega, $$ in a bounded domain $\Omega\subseteq \R^N$. Under suitable assumptions on $V_i$ and $P$, we prove the existence of ground-state solutions for this problem. Moreover, for $k=2$, assuming that the domain $\Omega$ and the potentials $V_i$ are radially symmetric, we prove that the ground state solutions are foliated Schwarz symmetric with respect to antipodal points. We provide several examples for our abstract framework.

Affiliated with

Also associated with

No associations

Rating

Existence and symmetry results for competing variational systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Existence and symmetry results for competing variational systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and symmetry results for competing variational systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-683153