Title: | Existence of solutions for a coupled system with $\phi $-Laplacian operators and nonlinear coupled boundary conditions (English) |

Author: | Goli, Konan Charles Etienne |

Author: | Adjé, Assohoun |

Language: | English |

Journal: | Communications in Mathematics |

ISSN: | 1804-1388 |

Volume: | 25 |

Issue: | 2 |

Year: | 2017 |

Pages: | 79-87 |

Summary lang: | English |

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Category: | math |

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Summary: | We study the existence of solutions of the system $$ \begin {cases} (\phi _1(u_1'(t)))'= f_1(t,u_1(t),u_2(t),u'_1(t),u_2'(t)),\qquad \text {a.e. $t\in [0,T]$}, (\phi _2(u_2'(t)))'= f_2(t,u_1(t),u_2(t),u'_1(t),u_2'(t)),\qquad \text {a.e. $t\in [0,T]$}, \end {cases} $$ submitted to nonlinear coupled boundary conditions on $[0,T]$ where $\phi _1,\phi _2\colon (-a, a)\rightarrow \mathbb {R}$, with $0 < a < +\infty $, are two increasing homeomorphisms such that $\phi _1(0) = \phi _2(0) = 0$, and $f_i:[0,T]\times \mathbb {R}^{4}\rightarrow \mathbb {R}$, $i\in \{1,2\}$ are two $L^1$-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result. (English) |

Keyword: | $\phi $-Laplacian; $L^1$-Carath\'eodory function; Schauder fixed-point Theorem. |

MSC: | 34B15 |

idZBL: | Zbl 1391.34052 |

idMR: | MR3745430 |

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Date available: | 2018-02-05T14:37:07Z |

Last updated: | 2020-01-05 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/147058 |

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