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GLOBAL SOLUTIONS TO A CLASS OF SECOND-ORDER DIFFERENTIAL EQUATIONS.
- Source :
-
Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ) . Jul2009, Vol. 34 Issue 2A, p147-160. 14p. - Publication Year :
- 2009
-
Abstract
- The aim of this paper is to review some classical results and present new theorems of existence and extend- ability of solutions to the following second-order nonlinear Cauchy problem: This equation cannot be represented in ASCII code value. where f : [0, T ] · R → R is continuous, derivative independent and T > 0, u0 , u1 are real numbers. We ?rst consider the model case of autonomous equations and some classical results are surveyed. Particular attention is then paid to the cases where f has either the form f (x, u) = q(x)ψ(u) or f (x, u) = h(x, u) + g(x, u) where ? is nondecreasing, h is dominated by nondecreasing functions in u while g looks like a contraction in the second argument. Methods based on the Leray-Schauder nonlinear alternative and the Krasnosel'skii ?xed point theorem are used to prove new existence theorems. Several examples and counterexamples illustrate the obtained results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 2193567X
- Volume :
- 34
- Issue :
- 2A
- Database :
- Academic Search Index
- Journal :
- Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. )
- Publication Type :
- Academic Journal
- Accession number :
- 51377821