Continuation theorems for periodic perturbations of autonomous systems

Abstract

ABSTRACT. It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equationin the space of periodic functions with fixed period w, can be computed in terms of the Brouwer degree of g. This result provides efficient continuation theorems specially for w-periodic perturbations of autonomous systems. Extensions to differential equations in flow-invariant ENR's are also given.

Periodic solutions of second order equations with asymptotical non-resonance

“…Now we compute d LS (id − L −1 N 0 , Ω, O). With a result of Capietto, Mawhin and Zanolin (see, Theorem 1 in [1]), we have…”

Solvability of Nonlocal Fractional Boundary Value Problems

“…Definition 2 (see [13]). The ]th fractional sum of defined on N , for ] > 0, is defined to be (4) where ∈ N +] . We also define the ]th fractional difference, where ] > 0 and 0 ≤…”

“…Rich results has been obtained due to the various powerful devices such as coincidence degree theory and cone theory. For details, see [1][2][3][4][5][6][7] and the references therein. Discrete fractional calculus has generated interest in recent years.…”

Index of solution set for perturbed Fredholm equations and existence of periodic solutions for delay differential equations

“…was chosen as the final point of homotopies. A detailed survey of related results and further developments can be found in [4].…”