## Handbook of Differential Equations: Ordinary Differential Equations: Ordinary Differential Equations (Google eBook)The 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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Anal apply assume assumptions asymptotic boundary value problems bounded cofactor compact condition consider constant continuous continuous function contradiction converges Corollary Darbouxian deﬁned deﬁnition deformation retract degree denote Dirichlet problem eigenvalue Equation 0.1 example exists exponential factors ﬁrst ﬁxed point ﬂow function given half-linear half-linear equation hence holds homeomorphism ifand implies inequality interval invariant algebraic curve isolating block Lemma limit cycles linear Liouvillian lower and upper lower solution Math method minimal nonlinear nonoscillation nonoscillatory nontrivial solution obtain ofthe ordinary differential equations oscillation oscillatory p-Laplacian partial differential equations polynomial vector field positive solutions principal solution proof of Theorem properties Proposition prove quadrics quasilinear radial Riccati equation satisﬁes satisfying second order Section sequence solution of 0.1 space strong deformation retract subset sufﬁciently Suppose T-periodic solution thatfor theory tion unique upper solutions vector field Wa˙zewski zero