Title | ASYMPTOTIC NONUNIFORM NONRESONANCE CONDITIONS FOR A NONLINEAR DISCRETE BOUNDARY VALUE PROBLEM |

Publication Type | Journal Article |

Year of Publication | 2008 |

Authors | MA RUYUN, O’REGAN DONAL |

Journal | Dynamic Systems and Applications |

Volume | 17 |

Start Page | 271 |

Pagination | 11 |

Date Published | 2008 |

ISSN | 1056-2176 |

AMS Subject Classification | 39A10 |

Abstract | Let T := {a+1, . . . , b+1}. We study the solvability of nonlinear discrete two-point boundary value problem ( ∆2u(t − 1) + g(t, u(t)) = h(t), t ∈ T, u(a) = u(b + 2) = 0 where h : T → R, g : T × R → R satisfies α(t) ≤ lim inf |x|→∞ x −1 g(t, x) ≤ lim sup |x|→∞ x −1 g(t, x) ≤ β(t) uniformly on T, and α and β satisfy some nonresonance conditions of nonuniform type with respect to two consecutive eigenvalues of the associated linear problem. The proof is based on the LeraySchauder continuation theorem. |

https://acadsol.eu/dsa/articles/17/DSA-2007-271-282.pdf | |

Refereed Designation | Refereed |