For a given pair of maps f, g : X → M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism Λfg : H(X) → H(M) of degree (−n). We prove a Lefschetztype coincidence theorem: if the Lefschetz homomorphism is nontrivial then there is an x ∈ X such that f(x) = g(x).

In this paper, I introduce the theorems in Professor Hukukane Nikaido’s work, “Coincidence and some systems of inequalities,” published in the Journal of Mathematical Society of Japan, 1959, and note the significance of his mathematical methods on the history and the future of mathematical economics. Nikaido (1959) may be considered a compilation of his works of the 1950’s on economic equilibri...

We study the entanglement between the two beams exiting a Mach-Zehnder interferometer fed by a couple of squeezed-coherent states with arbitrary squeezing parameter. The quantum correlations at the output are function of the internal phase-shift of the interferometer, with the output state ranging from a totally disentangled state to a state whose degree of entanglement is an increasing functio...

In this paper, we focus on the existence of solutions to a fractional boundary value problem at resonance. By constructing suitable operators, establish an theorem upon coincidence degree theory Mawhin.

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to topological (Nielsen) coincidence theory. We demonstrate that three natural axioms are sufficient to characterize the coincidence index in the setting of continuous m...

We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps. Introduction. In this paper we generalize the coincidence semi-index theory, introduced in [D-J] in the smooth case, to pairs of maps between topological manifolds. It will be based on the topological transversality lemma (...

In 1929, the KKMmap was introduced by Knaster et al. [13] and it provides the foundation for many well-known existence results, such as Ky Fan’s minimax inequality theorem, Ky Fan-Browder’s fixed point theorem, Nash’s equilibrium theorem, HartmanStampacchia’s variational inequality theorem and many others (see [1, 2, 5–12, 14–17]). The central idea of applying KKM theory to prove that a family ...

In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin’s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results. Keywords—Posi...