Mathematical Analysis of Intraguild Interactions among Hosts, Parasitoids and Predators

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.

Onm-accretive Schrödinger-type operators with singular potentials on manifolds of bounded geometry

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.