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On the oscillation of solutions of parabolic partial functional differential equations. (English) Zbl 0989.35131
Oscillation of solutions of parabolic functional differential equations is studied in the paper. The parabolic differential equations have continuous deviating arguments with the usual boundary value conditions. The method of proving oscillatory criteria is based on a reduction of the partial differential equation to an ordinary differential equation by using the first eigenfunction of the Laplacian together with the Green formula along with the Jensen integral inequality. The paper is finished with an illustrative example.
35R10 Partial functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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