Asymptotic solutions of forced nonlinear second order differential equations and their extensions
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2007-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2007/40/abstr.html |
| _version_ | 1819289947115356160 |
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| author | Angelo B. Mingarelli Kishin Sadarangani |
| author_facet | Angelo B. Mingarelli Kishin Sadarangani |
| author_sort | Angelo B. Mingarelli |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-24T03:14:56Z |
| format | Article |
| id | doaj.art-3bf7f18f3e16433e8122aa284ffed6f1 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-24T03:14:56Z |
| publishDate | 2007-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3bf7f18f3e16433e8122aa284ffed6f12022-12-21T17:17:40ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912007-03-01200740140Asymptotic solutions of forced nonlinear second order differential equations and their extensionsAngelo B. MingarelliKishin SadaranganiUsing 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.http://ejde.math.txstate.edu/Volumes/2007/40/abstr.htmlSecond order differential equationsnonlinearnon-oscillationintegral inequalitiesAtkinson's theoremasymptotically linearasymptotically constantoscillationdifferential inequalitiesfixed point theoremVolterra-Stieltjesintegral equations. |
| spellingShingle | Angelo B. Mingarelli Kishin Sadarangani Asymptotic solutions of forced nonlinear second order differential equations and their extensions Electronic Journal of Differential Equations 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. |
| title | Asymptotic solutions of forced nonlinear second order differential equations and their extensions |
| title_full | Asymptotic solutions of forced nonlinear second order differential equations and their extensions |
| title_fullStr | Asymptotic solutions of forced nonlinear second order differential equations and their extensions |
| title_full_unstemmed | Asymptotic solutions of forced nonlinear second order differential equations and their extensions |
| title_short | Asymptotic solutions of forced nonlinear second order differential equations and their extensions |
| title_sort | asymptotic solutions of forced nonlinear second order differential equations and their extensions |
| topic | 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. |
| url | http://ejde.math.txstate.edu/Volumes/2007/40/abstr.html |
| work_keys_str_mv | AT angelobmingarelli asymptoticsolutionsofforcednonlinearsecondorderdifferentialequationsandtheirextensions AT kishinsadarangani asymptoticsolutionsofforcednonlinearsecondorderdifferentialequationsandtheirextensions |