Maximal and minimal nondecreasing bounded solutions of iterative functional differential equations

Infinitely Many Positive Solutions to Nonlinear First-Order Iterative Systems of Singular BVPs on Time Scales

“…Iterative differential equations belong to functional differential equations. In particular, iterative equations can be used to describe functional differential equations with statedependent delays, see [1][2][3]. Iterative differential equations provide a new idea to study functional differential equations.…”

“…Iterative differential equations provide a new idea to study functional differential equations. Zhao and Liu [4] considered a class of iterative differential equation c 0 x (t) + c 1 x (t) + c 2 x(t) = x(p(t) + bx(t)) + h(t) (2) and obtained the existence, uniqueness, and stability of periodic solutions for Equation (2).…”

“…and obtained asymptotic properties of solutions. Fe ckan [6] further studied the following nonlinear iterative equation x (t) = f (x [2] (t))…”

"Positive periodic solutions for a class of first-order iterative differential equations with an application to a hematopoiesis model"

“…For instance, concerning first-order iterative differential equations, the author of this article and her co-author R. Khemis [7] discussed the existence of solutions for a first order delayed differential equation with an iterative source term that modelizes the evolution of an insect population, M. Fečkan and al. [10] recently studied the maximal and minimal nondecreasing bounded solutions for a first order iterative differential equation. The situation is the same with the higher order equations as very few contributions that have been made so far (see [4,5,6,8,13,14]).…”

Iterative system of nabla fractional difference equations with two-point boundary conditions

“…As a special type of state-dependent delaydifferential equations, iterative differential equations have distinctive characteristics and have been investigated in recent years, e.g., equivariance [38], analyticity [40], convexity [36], monotonicity [15], smoothness [11]. In [17], Fečkan, Wang and Zhao established the maximal and minimal nondecreasing bounded solutions of the following iterative functional differential equations z ′ (t) = g(t, z [1] (t), z [2] (t), . .…”