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Existence Theory for Nonlinear Ordinary Differential Equations: 398 (Mathematics and Its Applications, 398) - Hardcover
Synopsis
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
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Review
`I warmly recommend it to everyone interested in ordinary differential equations and its applications.'
Acta Sci. Math., 64 (1998)
Synopsis
This book presents an up-to-date account of many topics of interest in the theory of nonlinear ordinary differential equations. Topics include fixed point theory, periodic problems, lower and upper surfaces, positone and semi-positone problems, limit circle problems, finite and infinite interval problems and impulsive differential equations. In addition many important applications are presented to complement the theory.
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Existence Theory for Nonlinear Ordinary Differential Equations (Mathematics and Its Applications, 398)
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Existence Theory for Nonlinear Ordinary Differential Equations (Mathematics and Its Applications, 398, Band 398)
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Existence Theory for Nonlinear Ordinary Differential Equations
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further tha. Seller Inventory # 5968077
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Existence Theory for Nonlinear Ordinary Differential Equations (Mathematics and Its Applications, 398)
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Existence Theory for Nonlinear Ordinary Differential Equations
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Existence Theory for Nonlinear Ordinary Differential Equations
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Existence Theory for Nonlinear Ordinary Differential Equations
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Springer Netherlands Apr 1997, 1997
ISBN 10: 0792345118
ISBN 13: 9780792345114
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here. 212 pp. Englisch. Seller Inventory # 9780792345114
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Existence Theory for Nonlinear Ordinary Differential Equations
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here. Seller Inventory # 9780792345114
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Existence Theory for Nonlinear Ordinary Differential Equations
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ISBN 10: 0792345118
ISBN 13: 9780792345114
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Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 212 pp. Englisch. Seller Inventory # 9780792345114
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Existence Theory for Nonlinear Ordinary Differential Equations
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Condition: New. pp. 212. Seller Inventory # 26552566