| On Systems of Boundary Value Problems for Differential Inclusions |
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| 作者姓名： | Lynn ERBE Christopher C. TISDELL Patricia J. Y. WONG |
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| 作者单位： | [1]Department of Mathematics, The University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA [2]School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia [3]School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore |
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| 基金项目： | This research is supported by the Australian Research Council＇s Discovery Projects （DP0450752） and Linkage International （LX0561259） |
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| 摘 要： | Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.
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| 关 键 词： | 微分包含 边值问题 解 Bernstein-Nagumo条件 |
| 收稿时间： | 28 April 2005 |
| 修稿时间： | 2005-04-282006-05-14 |
On Systems of Boundary Value Problems for Differential Inclusions |
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| Lynn ERBE Christopher C. TISDELL Patricia J. Y. WONG.On Systems of Boundary Value Problems for Differential Inclusions[J].Acta Mathematica Sinica,2007,23(3):549-556. |
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| Authors: | Lynn Erbe Christopher C Tisdell Patricia J Y Wong |
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| Institution: | (1) Department of Mathematics, The University of Nebraska–Lincoln, Lincoln, NE 68588–0130, USA;(2) School of Mathematics and Statistics, The University of New South Wales, Sydney, 2052, Australia;(3) School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore |
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| Abstract: | Herein we consider the existence of solutions to second-order, two-point boundary value problems (BVPs) for systems of ordinary
differential inclusions. Some new Bernstein–Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems
for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs
without growth restrictions.
This research is supported by the Australian Research Council’s Discovery Projects (DP0450752) and Linkage International (LX0561259) |
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| Keywords: | boundary value problem systems of differential inclusions existence of solutions a priori bounds Bernstein-Nagumo condition |
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