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 ...
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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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Add this copy of Existence Theory for Nonlinear Ordinary Differential to cart. $159.69, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer.
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*Price HAS BEEN REDUCED by 10% until Monday, May 5 (weekend SALE item)* 207 pp., Hardcover, ex library, else text and binding clean and tight. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
Add this copy of Existence Theory for Nonlinear Ordinary Differential to cart. $83.21, very good condition, Sold by Orca Knowledge Systems, Inc rated 5.0 out of 5 stars, ships from Novato, CA, UNITED STATES, published 1997 by Springer.
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Very good. No DJ. Non circulating ex University of California, Berkeley reference library book with some library markings. Light wear. Binding is tight, text clean. From the back cover: Topics include fixed point theory, periodic problems, lower and upper survaces, positone and semi-positone problems, singular equations, limit circle problems, finite and infinite interval problems and impulsive differential equations.
Add this copy of Existence Theory for Nonlinear Ordinary Differential to cart. $118.65, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1997 by Springer.
Add this copy of Existence Theory for Nonlinear Ordinary Differential to cart. $159.69, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1997 by Springer.
Add this copy of Existence Theory for Nonlinear Ordinary Differential to cart. $186.87, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 1997 by Springer.
