POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

数学物理学报

POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

蔡果兰; 葛渭高

中央民族大学数学系, 北京 100081

收稿日期:2004-12-03 修回日期:2006-05-18 出版日期:2006-12-25 发布日期:2006-12-25
通讯作者: 蔡果兰
基金资助:
Supported by the National Natural Foundation of China (10371006) and the Youth Teachers Science Projects of Central University for Nationalities
(No.A08).

POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

Cai Guolan; Ge Weigao

Department of Mathematics, Central University for Nationalities, Beijing 100081, China

Received:2004-12-03 Revised:2006-05-18 Online:2006-12-25 Published:2006-12-25
Contact: Cai Guolan

摘要/Abstract

摘要： In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phi_p(u''(t)))''- f(t,u(t))=0, t≠ t_i,△ u(t_i)=-I_i(u(t_i)), i=1, 2, ..., k,△u'(t_i)=-L_i(u(t_i)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u''(0)=0=u''(1)-\phi_q(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.

关键词: Impulsive differential equation, BVP, P-Laplacian, Variable transform

Abstract: In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phi_p(u''(t)))''- f(t,u(t))=0, t≠ t_i,△ u(t_i)=-I_i(u(t_i)), i=1, 2, ..., k,△u'(t_i)=-L_i(u(t_i)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u''(0)=0=u''(1)-\phi_q(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.

Key words: Impulsive differential equation, BVP, P-Laplacian, Variable transform

中图分类号:

34B37

蔡果兰; 葛渭高. POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN[J]. 数学物理学报, 2006, 26(6): 1077-.

Cai Guolan; Ge Weigao. POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN[J]. Acta mathematica scientia,Series A, 2006, 26(6): 1077-.

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POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

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