Faculty of Mathematics and Computer Science

Nonlinear analysis |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Lect. BEGE Antal, Ph.D., bege@math.ubbcluj.ro |

Aims |

To present the basic discrete fixed point theorems and their applications to differential and integral equations. |

Content |

1. Fixed point theorems in ordered sets
2. Fixed point theorems in ordered Banach spaces 3. On the method of upper and lower solutions 4. Application to differential equations 5. Opial inequality and applications |

References |

1. A. Bege, Teoria discreta a punctului fixsi aplicatii, Presa Universitara, Cluj, 2002 (in curs de aparitie).
2. I. A Rus, generalized contractions and applications, Cluj University Press, 2001. 3. S. Heikkila, V. Laksmikantham, Monotone iterative techniques for discontinuous nonlinear differential equations, Marcel Dekker, New Zork, 1994. 4. R. V. Agarwal, P. Z. H. Pang, Opial inequalities with applicationsin differential and difference equations, Kluwer Academic Publisher, 1995. 5. S. Carl, S. Heikkila, Nonlinear differential equations in ordered spaces, Chapman and Hall, London, 2001. |

Assessment |

Exam |