Periodic solutions for a second order nonlinear functional differential equation

Abstract

The second order nonlinear delay differential equation with periodic coefficientsis considered in this work. By using Krasnoselskii's fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions to the delay differential equation.

On the existence of positive periodic solutions for totally nonlinear neutral differential equations of the second-order with functional delay

“…In view of the above differences between (1.1) and (1.2), our analysis is different from that in [20]. We refer to [5, 7-11, 14, 15], and [19] for results on some qualitative properties of neutral functional differential equations.…”

Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem

“…Existence, uniqueness, stability and positivity of solutions of functional differential equations are of great interest in mathematics and its applications to the modeling of various practical problems (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]) and references therein. Positivity is one of the most common and most important characteristics of mathematical models.…”

“…In the last 50 years, delay models are becoming more common, appearing in many branches of biological, economical and physical modelling (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]). This is due to their advantage of combining a simple, intuitive derivation with a wide variety of possible behavior regimes and to the fact that such models operate on an infinite dimensional space consisting of continuous functions that accommodate high dimensional dynamics (see [10][11][12]).…”

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

“…Existence, uniqueness, stability and positivity of solutions of functional differential equations are of great interest in mathematics and its applications to the modeling of various practical problems (see [1]- [14], [17]- [22], [24]- [25] and references therein). Positivity is one of the most common and most important characteristics of mathematical models.…”

“…In the last fifty years, delay models are becoming more common, appearing in many branches of biological, economical and physical modelling (see [1]- [22], [24], [25]). This is due to their advantage of combining a simple, intuitive derivation with a wide variety of possible behavior regimes and to the fact that such models operate on an infinite dimensional space consisting of continuous functions that accommodate high dimensional dynamics (see [14], [20]- [21]).…”