Oscillation of solutions of neutral partial functional differential equations
The authors use the generalized Riccati transformation in order to obtain sufficient conditions for an oscillation of the solutions to the following neutral partial differential-functional equations \[ {\partial \over \partial t}\left[p(t) {\partial\over\partial t}\left(u(x,t)+ \sum^\ell_{i=1} \lambda_i(t) u(x,t-\tau_i) \right)\right] = \] \[ =a(t)\Delta u(x,t)+\sum^s_{k=1} a_k(t)\Delta u\bigl(x,t- \rho_k(t)\bigr) -q(x,t)u(x,t)- \] \[ -\sum^m_{j=1}q_j (x,t)f_j \bigl(u(x,t -\sigma_j)\bigr), \quad(x,t)\in\Omega \times [0,\infty), \] with boundary conditions of mixed type or Dirichlet type.
scientific article; zbMATH DE number 1309050