positivity of solution
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2021 ◽  
Vol 52 (1) ◽  
pp. 171-187
Author(s):  
Hongming You ◽  
Kaijen Cheng

In this work, we consider a mathematical model of an omnivorous ecosystem in which intermediate predators are infected by parasites. We first establish the boundeness and positivity of solution with conditions. Then the existence and local stability of all equilibria are clarified in R4. Finally, some global dynamics will be analyzed.  



2003 ◽  
Vol 2003 (38) ◽  
pp. 2415-2423 ◽  
Author(s):  
Ognjen Milatovic

We consider a Schrödinger-type differential expression∇∗ ∇+V, where∇is aC∞-bounded Hermitian connection on a Hermitian vector bundleEof bounded geometry over a manifold of bounded geometry(M,g)with positiveC∞-bounded measuredμ, andVis a locally integrable linear bundle endomorphism. We define a realization of∇∗ ∇+VinL2(E)and give a sufficient condition for itsm-accretiveness. The proof essentially follows the scheme of T. Kato, but it requires the use of a more general version of Kato's inequality for Bochner Laplacian operator as well as a result on the positivity of solution to a certain differential equation onM.



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