Angelo B. Mingarelli, Kishin Sadarangani
Abstract:
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.
Submitted February 15, 2007. Published March 9, 2007.
Math Subject Classifications: 39A11, 34E10, 34A30, 34C10, 45D05, 45G10, 45M05.
Key Words: 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.
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Angelo B. Mingarelli School of Mathematics and Statistics Carleton University, Ottawa, Ontario, K1S 5B6, Canada Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain email: amingare@math.carleton.ca amingarelli@dma.ulpgc.es |
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Kishin Sadarangani Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain email: ksadaran@dma.ulpgc.es |
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