2020
DOI: 10.3906/mat-2004-52
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Positive periodic solutions for a class of second-order differential equations with state-dependent delays

Abstract: In this paper, we consider a class of second order differential equations with iterative source term. The main results are obtained by virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green's function which allows us to prove the existence of positive periodic solutions. Finally, an example is included to illustrate the correctness of our results.

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Cited by 13 publications
(3 citation statements)
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“…[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]).…”
Section: Introductionmentioning
confidence: 73%
“…[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]).…”
Section: Introductionmentioning
confidence: 73%
“…For detailed information about such equations and their emerging theory we refer the reader to [1][2][3][4][5][6][7][8][9][10][11][12], [14][15][16][17].…”
Section: Introductionmentioning
confidence: 99%
“…In [7], by virtue of the Krasnoselskii's fixed point theorem, the authors proved the existence of positive periodic solutions for the following second-order iterative differential equation;…”
Section: Introductionmentioning
confidence: 99%