| POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN |
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| 作者姓名： | 蔡果兰 葛渭高 |
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| 作者单位： | 中央民族大学数学系, 北京 100081 |
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| 基金项目： | Supported by the National Natural Foundation of China (10371006) and the Youth Teachers Science Projects of Central University for Nationalities
(No.A08). |
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| 摘 要： | In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phip(u'(t)))'- f(t,u(t))=0, t≠ ti,△ u(ti)=-Ii(u(ti)), i=1, 2, ..., k,△u'(ti)=-Li(u(ti)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u'(0)=0=u'(1)-\phiq(α)u'(η),the authors translate the fourth-order impulsive differential equations with p-Laplacian (\star) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (\star) are obtained.
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| 关 键 词： | Impulsive differential equation BVP P-Laplacian Variable transform |
| 收稿时间： | 2004-12-03 |
| 修稿时间： | 2006-05-18 |
POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN |
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| Cai Guolan,Ge Weigao.POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN[J].Acta Mathematica Scientia,2006,26(6):1077. |
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| Authors: | Cai Guolan Ge Weigao |
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| Institution: | Department of Mathematics, Central University for Nationalities, Beijing 100081, China |
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| Abstract: | In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phip(u'(t)))'- f(t,u(t))=0, t≠ ti,△ u(ti)=-Ii(u(ti)), i=1, 2, ..., k,△u'(ti)=-Li(u(ti)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u'(0)=0=u'(1)-\phiq(α)u'(η),the authors translate the fourth-order impulsive differential equations with p-Laplacian (\star) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (\star) are obtained. |
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| Keywords: | Impulsive differential equationzz BVPzz P-Laplacianzz Variable transformzz |
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