Oscillation of delay parabolic differential equations with several coefficients. (English) Zbl 1011.35125

Summary: Some new sufficient conditions are established for the oscillation of delay parabolic differential equations of the form \[ {\partial u (x,t) \over\partial t}= a(t)\Delta u-\sum^n_{i=1} p_i(x,t)u(x,t-\sigma_i)+ \sum^m_{j=1} q_j(x,t) u(x,t-\tau_j), \tag{1} \] \((x,t)\in\Omega \times[t_0, \infty) \equiv G\) where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with a piecewise smooth boundary \(\partial\Omega\), and \(\Delta\) is the Laplacian in Euclidean \(n\)-space \(\mathbb{R}^n\) with three different boundary conditions. Our results improve the well-known oscillation result of (1) when \(n=m=1\). An example is considered to illustrate our main results.


35R10 Partial functional-differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35K15 Initial value problems for second-order parabolic equations
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