Fixed point theory for compact absorbing contractive admissible type maps

In this article we present new Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Fréchet spaces. Also, we discuss condensing maps with a compact attractor. Finally we present new antipodal fixed point theory for Kakutani maps.     

Coincidence degree theory for mappings of class L − (S +)

In this article, we introduce the multi-valued mapping of class L-(S₊) in a Hilbert space and construct a coincidence degree theory for such a mapping.     

Fixed point theory in Fréchet spaces for Volterra type operators

New fixed point theorems for maps (single and multivalued) between Fréchet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence of Banach spaces.     

Asymptotic properties and simulations of a stochastic single-species dispersal model under regime switching

Taking both white noise and colored environmental noise into account, a single-species logistic model with population’s nonlinear diffusion among two patches is proposed and investigated. The sufficient conditions of the existence of positive solutions, stochastic permanence, persistence in mean and extinction are established. Moreover, we use an example and simulation figures to illustrate our main results.     

Choking Horns in Lipschitz Geometry of Complex Algebraic Varieties. Appendix by Walter D. Neumann

The paper studies the Lipschitz geometry of germs of complex algebraic varieties and introduces the notion of a choking horn. A choking horn is a family of cycles on an algebraic variety with the property that the cycles cannot be boundaries of nearby chains. The presence of choking horns is an obstruction to metric conicalness and the authors use this to prove that some classical isolated hypersurface singularities are not metrically conical. They also show that there exist countably infinitely many singular varieties, which are locally homeomorphic, but not locally subanalytically bi-Lipschitz equivalent with respect to the inner metric. The Appendix by W. Neumann uses separating sets to provide another example of the same phenomenon.     

Applications of linking to Hammerstein integral equations

In this paper we establish some results for asymptotic linear Hammerstein integral equations using the notion of linking (both homotopical and (co) homological).