Title | POSITIVE PERIODIC SOLUTIONS OF SECOND-ORDER SYSTEMS WITH SINGULARITIES AND DEVIATING ARGUMENTS |

Publication Type | Journal Article |

Year of Publication | 2016 |

Authors | BESSIOUD, KARIMA, ARDJOUNI, ABDELOUAHEB, DJOUDI, AHCENE |

Secondary Title | Communications in Applied Analysis |

Volume | 20 |

Issue | 2 |

Start Page | 223 |

Pagination | 15 |

Date Published | 06/2016 |

Type of Work | scientific: mathematics |

ISSN | 1083-2564 |

AMS | 34B16, 34B18, 34B27, 34K13, 47H10 |

Abstract | In this paper, we use Schauder’s fixed point theorem to prove that the second-order systems with singularities and deviating arguments $$( x ′′ (t) + a1 (t) x (t) = f1 (t, y (t − τ1 (t))) + e1 (t), $$ $$y ′′ (t) + a2 (t) y (t) = f2 (t, x (t − τ2 (t))) + e2 (t),$$ has a positive periodic solution, where ai , τi ∈ L 1 (R/TZ, R+), ei ∈ L 1 (R/TZ, R) and fi (i = 1, 2) are Carath´eodory functions and have singularities at the origin. An example is also given to illustrate our work. |

URL | http://www.acadsol.eu/en/articles/20/2/4.pdf |

DOI | 10.12732/caa.v20i4.1 |

Full Text | REFERENCES [1] J. Chu, N. Fan and P. J. Torres, Periodic solutions for second order singular damped differential equations, J. Math. Anal. Appl. 388 (2012) 665–675. |