ERIC Number: EJ894156
Record Type: Journal
Publication Date: 2010
Abstractor: As Provided
Reference Count: 10
Bounded Solutions to x[double prime] + q(t)b(x) = f(t)
Kroopnick, Allan J.
International Journal of Mathematical Education in Science and Technology, v41 n6 p829-836 2010
This article discusses the conditions under which all solutions to x[double prime] + q(t)b(x) = f(t) are bounded on [0, [infinite]]. These results are generalizations of the linear case. A short discussion of the properties of bounded oscillatory solutions for both the linear and nonlinear cases when f(t) = 0, xb(x) greater than 0 and b[prime](x) greater than 0 for x [is not equal to] 0 is also provided. Finally, we shall see that the previous arguments may be applied to the more general nonlinear differential equation x[double prime] + c(t, x, x[prime]) + q(t)b(x) = f(t) with appropriate conditions on c(t, x, x[prime]).
Descriptors: Calculus, Problem Solving, Mathematics Instruction, Equations (Mathematics), Validity, Mathematical Logic, Generalization
Taylor & Francis, Ltd. 325 Chestnut Street Suite 800, Philadelphia, PA 19106. Tel: 800-354-1420; Fax: 215-625-2940; Web site: http://www.tandf.co.uk/journals
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Authoring Institution: N/A