Qualitative Analysis of Dynamic Activity Patterns in Neural Networks

Abstract

An abstract second order differential equation such that the linear part of the right-hand side is given by the infinitesimal generator of a strongly continuous cosine family of bounded linear operators while the nonlinear part satisfies a global Lipschitz condition, and provided with impulse and nonlocal conditions is studied. Theorems for existence and uniqueness of a mild and classical solution of the problem considered are proved.