Calculus of Variations and Partial Differential Equations

, Volume 31, Issue 1, pp 1–25

Solutions with multiple spike patterns for an elliptic system

Original Article

DOI: 10.1007/s00526-007-0103-z

Cite this article as:
Ramos, M. & Tavares, H. Calc. Var. (2008) 31: 1. doi:10.1007/s00526-007-0103-z

Abstract

We consider a system of the form \(- \varepsilon^2 \Delta u + V(x)u=g(v)\) , \(-\varepsilon^2 \Delta v + V(x)v=f(u)\) in an open domain \(\Omega\) of \( {\mathbb{R}}^N\) , with Dirichlet conditions at the boundary (if any). We suppose that f and g are power-type non-linearities, having superlinear and subcritical growth at infinity. We prove the existence of positive solutions \(u_{\varepsilon}\) and \(v_{\varepsilon} \) which concentrate, as \(\varepsilon\to 0\) , at a prescribed finite number of local minimum points of V(x), possibly degenerate.

Mathematics Subject Classification (2000)

35J5058E05

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.University of Lisbon, CMAF, Faculty of ScienceLisboaPortugal