Variational Methods in Nonlinear Field Equations
The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,.). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.
Provides existence and stability results for solitary waves, solitons and vortices in variational nonlinear PDE’sTheory sufficiently general and flexible to be applied to many other situationsApplications to the existence of solitons in the nonlinear beam equation and to the study of vorticesContains a general existence theory for hylomorphic solitonsSummarizes the main results obtained in the last 35 years