## Handbook of Differential Equations: Ordinary Differential Equations, Volume 1The book contains seven survey papers about ordinary differential equations. The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations. The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications. |

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### Contents

69 | |

Chapter 3 Halflinear differential equations | 161 |

Chapter 4 Radial solutions of quasilinear elliptic differential equations | 359 |

Chapter 5 Integrability of polynomial differential systems | 437 |

Chapter 6 Global results for the forced pendulum equation | 533 |

Chapter 7 Ważewski method and Conley index | 591 |

Author Index | 685 |

693 | |

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a.e. t e assume assumptions asymptotic boundary value problems bounded cofactor compact condition consider constant continuous function contradiction converges Corollary Darbouxian defined definition deformation retract degree denote Dirichlet problem eigenvalue Equation 0.1 Equation 23 exists exponential factors fixed point index given half-linear equation hence holds homeomorphism implies inequality interval invariant algebraic curve isolating block Lemma limit cycles linear Liouvillian lower and upper lower solution Math minimal nonoscillation nonoscillatory nontrivial solution obtain ordinary differential equations oscillation oscillatory p-Laplacian partial differential equations periodic solutions polyfacial set polynomial system polynomial vector field positive solutions principal solution proof of Theorem properties Proposition prove quasilinear Riccati equation satisfies second order Section sequence solution of 0.1 space subset Suppose t e a,b t-Co T-periodic theory tion topological unique upper solutions vector field zero