Memoirs of the American Mathematical Society 2013; 89 pp; softcover Volume: 229 ISBN10: 0821891634 ISBN13: 9780821891636 List Price: US$71 Individual Members: US$42.60 Institutional Members: US$56.80 Order Code: MEMO/229/1076
 The authors study the following singularly perturbed problem: \(\epsilon^2\Delta u+V(x)u = f(u)\) in \(\mathbf{R}^N\). Their main result is the existence of a family of solutions with peaks that cluster near a local maximum of \(V(x)\). A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities \(f\). Table of Contents  Introduction and results
 Preliminaries
 Local centers of mass
 Neighborhood \(\Omega_\epsilon(\rho,R,\beta)\) and minimization for a tail of \(u\) in \(\Omega_\epsilon\)
 A gradient estimate for the energy functional
 Translation flow associated to a gradient flow of \(V(x)\) on \({\bf R}^N\)
 Iteration procedure for the gradient flow and the translation flow
 An \((N+1)\ell_0\)dimensional initial path and an intersection result
 Completion of the proof of Theorem 1.3
 Proof of Proposition 8.3
 Proof of Lemma 6.1
 Generalization to a saddle point setting
 Bibliography
