Title: | Existence of multiple solutions for some functional boundary value problems (English) |

Author: | Staněk, Svatoslav |

Language: | English |

Journal: | Archivum Mathematicum |

ISSN: | 0044-8753 (print) |

ISSN: | 1212-5059 (online) |

Volume: | 28 |

Issue: | 1 |

Year: | 1992 |

Pages: | 57-65 |

Summary lang: | English |

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Category: | math |

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Summary: | Let $X$ be the Banach space of $C^0$-functions on $\langle 0,1\rangle $ with the sup norm and $\alpha ,\beta \in X \rightarrow {R}$ be continuous increasing functionals, $\alpha (0)= \beta (0)=0$. This paper deals with the functional differential equation (1) $x^{\prime \prime \prime } (t) = Q [ x, x^\prime , x^{\prime \prime }(t)] (t)$, where $Q:{X}^2 \times {R} \rightarrow {X}$ is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions $\alpha (x)=0=\beta (x^\prime )$, $x^{\prime \prime }(1)-x^{\prime \prime }(0)=0$ are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional differential equations. (English) |

Keyword: | Schauder linearization technique |

Keyword: | Schauder differential equation |

Keyword: | functional boundary conditions |

Keyword: | boundary value problem |

MSC: | 34B10 |

MSC: | 34B15 |

idZBL: | Zbl 0782.34074 |

idMR: | MR1201866 |

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Date available: | 2008-06-06T21:04:48Z |

Last updated: | 2012-05-10 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/107436 |

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