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Oscillatory and periodic solutions to a diffusion equation of neutral type. (English) Zbl 0935.35006

The authors prove many interesting theorems concerning boundary value problems for partial differential equations with piecewise constant argument. It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without delay. The properties of both periodic and oscillatory solutions are discussed, and the existence of solutions asymptotically approaching closed curves which are not solutions of the given equation is also discussed. This is an important contribution of the authors to the area of the partial differential equations with piecewise constant delay.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35R10 Partial functional-differential equations
35B10 Periodic solutions to PDEs
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