Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters (original) (raw)

Periodic and almost periodic solutions of integral equations

Applied Mathematics and Computation, 1999

Existence principles are presented which guarantee the existence of a continuous periodic or continuous almost periodic solution y of the nonlinear Fredholm integral equation: yt ht s ktY sf sY ys dsY t P sX

Periodic solutions of partial functional differential equations

2021

In this paper we study the existence of periodic solutions to the partial functional differential equation { dy(t) dt = By(t) + L̂(yt) + f(t, yt), ∀t ≥ 0, y0 = φ ∈ CB . where B : Y → Y is a Hille-Yosida operator on a Banach space Y . For CB := {φ ∈ C([−r, 0];Y ) : φ(0) ∈ D(B)}, yt ∈ CB is defined by yt(θ) = y(t + θ), θ ∈ [−r, 0], L̂ : CB → Y is a bounded linear operator, and f : R×CB → Y is a continuous map and is T -periodic in the time variable t. Sufficient conditions on B, L̂ and f(t, yt) are given to ensure the existence of T -periodic solutions. The results then are applied to establish the existence of periodic solutions in a reaction-diffusion equation with time delay and the diffusive Nicholson’s blowflies equation.

On continua of periodic solutions for functional differential equations

Rocky Mountain Journal of Mathematics, 1977

0. Introduction. Recently, certain arguments which originated in asymptotic fixed point theory have been used with remarkable success in the study of functional differential equations by G. S. Jones [10], S. N. Chow [3] and R. D. Nussbaum [14, 15, 16]. Our observations here are in this line and are directly motivated by results of Nussbaum in [ 14]. He considers differential-delay equations which can be transformed to the form x '(t) =-\f(x(t-1)). Our approach here will be to obtain an abstract existence result providing a continuum of non-trivial solutions for a nonlinear eigenvalue problem F(x, A) = x and apply it to obtain a continuum of nontrivial periodic solutions for certain differential-delay equations. Our abstract theorem is based on a kind of asymptotic version of Krasnosel'skiï's results in [11,12] on expansions and compressions of a cone in a Banach space and this is due to G. Fournier and the author. The application then substantially relies on earlier work of E. M. Wright [20] and R. D. Nussbaum [14].

Periodic solutions of first order functional differential equations

2011

We study the existence of T-periodic solutions of some first order functional differential equations. Several existence criteria are established for our problems; in particular, we obtain conditions for the existence of multiple (even infinitely many) T-periodic solutions of one of the problems. Examples are also included to illustrate our results.

Periodic solutions for functional–differential equations of mixed type

Journal of Mathematical Analysis and Applications, 2007

In this paper we study the existence of ω-periodic solutions for some functional-differential equations of mixed type. Among the main results are the averaging principle and existence theorems for some equations with homogeneous nonlinearities. We use here the coincidence degree theory of Mawhin.