## A Topological Introduction to Nonlinear Analysis"The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory . . . reading is fluid and very pleasant . . . style is informal but far from being imprecise." —MATHEMATICAL REVIEWS (Review of the First Edition) Here is a book that will be a joy to the mathematician or graduate student of mathematics---or even the well-prepared undergraduate---who would like, with a minimum of background and preparation, to understand some of the beautiful results at the heart of nonlinear analysis. Based on carefully expounded ideas from several branches of topology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in providing its readers with an understanding of the mathematics of the nonlinear phenomena that characterize our real world. New to the second edition: New chapters will supply additional applications of the theory and techniques presented in the book. * Several new proofs, making the second edition more self-contained. |

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### Contents

The Topological Point of View | 3 |

AscoliArzela Theory | 9 |

Brouwer Fixed Point Theory | 19 |

Schauder Fixed Point Theory | 23 |

The Forced Pendulum | 29 |

Equilibrium Heat Distribution | 39 |

Generalized Bernstein Theory | 45 |

Degree Theory | 49 |

A Separation Theorem | 95 |

Compact Linear Operators | 99 |

The Degree Calculation | 111 |

The KrasnoselskiiRabinowitz Bifurcation Theorem | 119 |

Nonlinear SturmLiouville Theory | 133 |

More SturmLiouville Theory | 143 |

Euler Buckling | 155 |

Appendices | 161 |

Brouwer Degree | 51 |

Properties of the Brouwer Degree | 55 |

LeraySchauder Degree | 63 |

Properties of the LeraySchauder Degree | 69 |

The Mawhin Operator | 79 |

The Pendulum Swings Back | 85 |

Bifurcation Theory | 93 |

Singular Homology | 163 |

Additivity and Product Properties | 169 |

Bounded Linear Transformations | 175 |

181 | |

183 | |