ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We consider the problem where a and f are 1-periodic in t, a is positive, f satisfies appropriate decreasing conditions; smoothness of a, f, ∂Ω is also assumed. Denote by λ0 the principal eigenvalue of Δ with zero Dirichlet boundary conditions, and define . We prove: (a) if ε ≤ 0, then no non-negative periodic solution exists but zero, and any solution with continuous non-negative initial datum converges to zero uniformly as t → ∞; (b) if ε 〉 0, then a unique non trivial non-negative 1-periodic solution u* exists, and any solution with continuous, non-negative not identically zero initial datum approaches uniformly u* as t → ∞.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670030103
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