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

Abstract

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

CLC Number:

34B37

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-.

Trendmd

[1]	Chen Lin. Multiple Solutions for a Quasilinear Elliptic System of Kirchhoff Type [J]. Acta mathematica scientia,Series A, 2017, 37(4): 671-683.
[2]	Chen Huiwen, Li Jianli, Shen Jianhua. New Results for Neumann Boundary Value Problem with Impulses via Variational Methods [J]. Acta mathematica scientia,Series A, 2017, 37(1): 54-61.
[3]	JIN Yong-Yang. Nonexistence Results for a Class of Sub-P-Laplacians [J]. Acta mathematica scientia,Series A, 2009, 29(5): 1434-1441.
[4]	GAI Yong-Jie, JIANG Da-Qing, ZU Li, WENG Shi-You, WEI Jun. Positive Solution of Semipositone Singular Dirichlet Boundary Value Problems for Second Order Impulsive Differential Equations [J]. Acta mathematica scientia,Series A, 2009, 29(5): 1415-1425.
[5]	Lin Lishan;Li Yongqing. Existence of Solutions of Nonlinear Eigenvalue Problems Laplacian and Weights [J]. Acta mathematica scientia,Series A, 2007, 27(6): 996-1005.
[6]	Xiong Ming; Liu Jiaquan; Zeng Pingan. Positive Solutions for Singular Two-point Boundary Value Problem for p-Laplacian Equation [J]. Acta mathematica scientia,Series A, 2007, 27(3): 549-558.
[7]	Liu Xiangqing; Huang Yisheng. A Class of Quasilinear Elliptic Equations with Weights [J]. Acta mathematica scientia,Series A, 2007, 27(2): 277-287.
[8]	Zhang Xiaoyan;Sun Jingxian. Existence of Multiple Solutions for the One-dimensional Singular p-Laplacian Equations [J]. Acta mathematica scientia,Series A, 2006, 26(1): 143-149.
[9]	ZHANG Yu, WANG Chun-Yan, SUN Ji-Chao. Stability of Impulsive Differential Equations with Impulses at Variable Times [J]. Acta mathematica scientia,Series A, 2005, 25(6): 777-783.
[10]	BAI Ding-Yong, MA Ru-Yun. The Existence of Positive Solutions for a Singular Boundary Value Problem with p Laplacian Operator [J]. Acta mathematica scientia,Series A, 2005, 25(2): 166-170.
[11]	LI Bi-Wen. The Existence of Positive Solutions of Singular Boundary Value Problems with p-Laplacian [J]. Acta mathematica scientia,Series A, 2003, 23(3): 257-264.
[12]	Xu Genqi. INTEGRATED BISEMIGROUP AND APPLICATIONS TO IMPULSIVE DIFFERENTIAL EQUATIONS [J]. Acta mathematica scientia,Series A, 1997, 17(S1): 206-210.

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

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 12

Metrics

Comments

Recommended 10