Oscillatory properties of solutions of nonlinear parabolic equations with functional arguments (Q1430944)

This very interesting paper treats the oscillatory properties of the solutions to the following nonlinear parabolic equation with functional arguments \[ \frac{\partial}{\partial t} \left( u(x,t) + \sum_{i=1}^l h_i(t) u(x,\tau_i(t)) \right) - a(t)\Delta u \] \[ + \;q(x,t) f(u(x,\sigma(t))) = 0, \qquad (x,t) \in G \times \mathbb{R}_+ \] subject to homogeneous Dirichlet or mixed boundary condition. The authors reduce the multi-dimensional problem to a one-dimensional one by using integral means of solutions. Adequate examples illustrate the obtained results.