## Oscillation of partial population model with diffusion and delay.(English)Zbl 1182.35219

Summary: By using the upper- and lower-solution method of partial functional differential equations and the oscillation theory of functional differential equation, the oscillation of a population equation with diffusion and delay is studied and a sufficient condition for all positive solutions of the equation to oscillate about the positive equilibrium is obtained. Finally, a model arising from ecology is given to illustrate the obtained results.

### MSC:

 35Q92 PDEs in connection with biology, chemistry and other natural sciences 35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) 35A15 Variational methods applied to PDEs 92D40 Ecology
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### References:

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