Asymptotic solutions of forced nonlinear second order differential equations and their extensions
Mingarelli, Angelo B.
Texas State University-San Marcos, Department of Mathematics
Using a modified version of Schauder's fixed point theorem, measures of non-compactness and classical techniques, we provide new general results on the asymptotic behavior and the non-oscillation of second order scalar nonlinear differential equations on a half-axis. In addition, we extend the methods and present new similar results for integral equations and Volterra-Stieltjes integral equations, a framework whose benefits include the unification of second order difference and differential equations. In so doing, we enlarge the class of nonlinearities and in some cases remove the distinction between superlinear, sublinear, and linear differential equations that is normally found in the literature. An update of papers, past and present, in the theory of Volterra-Stieltjes integral equations is also presented.
Second order differential equations, Nonlinear, Non-oscillation, Integral inequalities, Atkinson's theorem, Asymptotically linear, Asymptotically constant, Oscillation, Differential inequalities, Fixed point theorem, Volterra-Stieltjes, Integral equations
Mingarelli, A. B., & Sadarangani, K. (2007). Asymptotic solutions of forced nonlinear second order differential equations and their extensions. <i>Electronic Journal of Differential Equations, 2007</i>(40), pp. 1-40.