Locating the peaks of semilinear elliptic systems
Abstract
We consider a system of weakly coupled singularly perturbed semilinear elliptic equations. First, we obtain a Lipschitz regularity result for the associated ground energy function $\Sigma$ as well as representation formulas for the left and the right derivatives. Then, we show that the concentration points of the solutions locate close to the critical points of $\Sigma$ in the sense of subdifferential calculus.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2005
 DOI:
 10.48550/arXiv.math/0506139
 arXiv:
 arXiv:math/0506139
 Bibcode:
 2005math......6139P
 Keywords:

 Mathematics  Analysis of PDEs;
 35J65;
 35Q40;
 35Q55;
 83C50
 EPrint:
 To appear on Advanced Nonlinear Studies, 21 pages