Positive Solutions of n th-Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions

Academic Editor: Feliz Manuel Minhós Copyright q 2011 Meiqiang Feng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper is devoted to study the existence, nonexistence, and multiplicity of positive solutions for the nth-order nonlocal boundary value problem with impulse effects. The arguments are based upon fixed point theorems in a cone. An example is worked out to demonstrate the main results.

[1]  Weigao Ge,et al.  Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces , 2010, J. Comput. Appl. Math..

[2]  Zhanbing Bai,et al.  Positive solutions of some nonlocal fourth-order boundary value problem , 2010, Appl. Math. Comput..

[3]  Weigao Ge,et al.  Positive solutions of nth-order impulsive boundary value problems with integral boundary conditions in Banach spaces , 2009 .

[4]  Weigao Ge,et al.  Existence results for a class of nth order m-point boundary value problems in Banach spaces , 2009, Appl. Math. Lett..

[5]  Weigao Ge,et al.  Positive solutions for a class of boundary-value problems with integral boundary conditions , 2009, Comput. Math. Appl..

[6]  Weigao Ge,et al.  Impulsive boundary value problems with integral boundary conditions and one-dimensional p-Laplacian , 2009 .

[7]  W. Ge,et al.  Impulsive boundary value problems involving the one-dimensional p-Laplacian☆ , 2009 .

[8]  Bashir Ahmad,et al.  Existence Results for Nonlinear Boundary Value Problems of Fractional Integrodifferential Equations with Integral Boundary Conditions , 2009 .

[9]  Huihui Pang,et al.  A class of three-point boundary-value problems for second-order impulsive integro-differential equations in Banach spaces , 2009 .

[10]  Weigao Ge,et al.  Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces , 2008 .

[11]  Jingbao Yang,et al.  Positive solutions of nth order m-point boundary value problem , 2008, Appl. Math. Comput..

[12]  Xinguang Zhang,et al.  A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with p-Laplacian , 2008 .

[13]  Daniel Franco,et al.  Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions , 2008, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[14]  Zhanbing Bai.  ITERATIVE SOLUTIONS FOR SOME FOURTH-ORDER PERIODIC BOUNDARY VALUE PROBLEMS , 2008 .

[15]  Zhanbing Bai.  The upper and lower solution method for some fourth-order boundary value problems☆ , 2007 .

[16]  Weigao Ge,et al.  Positive solutions for a class of m-point singular boundary value problems , 2007, Math. Comput. Model..

[17]  Lishan Liu,et al.  Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems , 2007 .

[18]  Daqing Jiang,et al.  Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations , 2006 .

[19]  Zhanquo Bai,et al.  Existence of Positive Solutions to Fourth Order Quasilinear Boundary Value Problems , 2006 .

[20]  M. Benchohra,et al.  Impulsive differential equations and inclusions , 2006 .

[21]  Bashir Ahmad,et al.  Positive solutions of a nonlinear nth order boundary value problem with nonlocal conditions , 2005, Appl. Math. Lett..

[22]  Jingli Ren,et al.  Positive solution for m-point boundary value problems , 2005 .

[23]  Bai,et al.  POSITIVE SOLUTIONS OF m-POINT BOUNDARY-VALUE PROBLEMS , 2005 .

[24]  Eun Kyoung Lee,et al.  Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations , 2004, Appl. Math. Comput..

[25]  Ruyun Ma,et al.  Positive solutions for nonlinear m-point Eigenvalue problems , 2004 .

[26]  Weigao Ge,et al.  Positive solutions for three-point boundary value problems with dependence on the first order derivative☆ , 2004 .

[27]  Haiyan Wang,et al.  Positive solutions of nonlinear three-point boundary-value problems , 2003 .

[28]  Weigao Ge,et al.  Triple Solutions for Second-order Three-point Boundary Value Problems , 2002 .

[29]  Bing Liu,et al.  Existence of solution for m-point boundary value problems of second-order differential systems with impulses , 2002, Appl. Math. Comput..

[30]  Ravi P. Agarwal,et al.  Multiple nonnegative solutions for second order impulsive differential equations , 2000, Appl. Math. Comput..

[31]  C. P. Gupta,et al.  A generalized multi-point boundary value problem for second order ordinary differential equations , 1998 .

[32]  Wenying Feng,et al.  On an M -point boundary value problem , 1997 .

[33]  Wenying Feng,et al.  Solvability of three point boundary value problems at resonance , 1997 .

[34]  J. Webb,et al.  Solvability ofm-Point Boundary Value Problems with Nonlinear Growth , 1997 .

[35]  Wang Haiyan,et al.  On the Existence of Positive Solutions of Fourth-Order Ordinary Differential Equations , 1995 .

[36]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[37]  W. Ames,et al.  Nonlinear problems in abstract cones , 1988 .

[38]  J. R. Cannon,et al.  The solution of the heat equation subject to the specification of energy , 1963 .