Necessary and sufficient conditions for oscillation of Robin boundary problems of neutral functional parabolic equations (Q1860387)

The goal of the paper is to give some necessary and sufficient conditions for oscillation of neutral parabolic equations with deviating arguments of the form \[ {\partial\over \partial t}\left[u(x,t)-\sum^L_{k=1}\lambda_k (t)u(x,t-\tau_k) \right]= a(t)\Delta u(x,t)+ \sum^m_{i=1} a_i(t)\Delta u\bigl(x,p_i(t) \bigr)-\sum^r_{j=1} q_j(t)u\bigl( x,\sigma_j(t) \bigr), \] where \((x,t)\in\Omega\times[0,\infty)\). \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with piecewise smooth boundary \(\partial\Omega\), and \(\Delta\) is the Laplacian in the Euclidean \(n\)-space \(\mathbb{R}^n\).