Solutions of Second-Order m-Point Boundary Value Problems for Impulsive Dynamic Equations on Time Scales

We study a general second-order -point boundary value problems for nonlinear singular impulsive dynamic equations on time scales , , and The existence and uniqueness of positive solutions are established by using the mixed monotone fixed point theorem on cone and Krasnosel’skii fixed point theorem. In this paper, the function items may be singular in its dependent variable. We present examples to illustrate our results.

[1]  Lianggen Hu,et al.  Positive solutions to singular third-order three-point boundary value problems on time scales , 2010, Math. Comput. Model..

[2]  Yuanyuan Pang,et al.  Upper and lower solution method for a fourth-order four-point boundary value problem on time scales , 2009, Appl. Math. Comput..

[3]  Sihua Liang,et al.  The existence of three positive solutions of m-point boundary value problems for some dynamic equations on time scales , 2009, Math. Comput. Model..

[4]  Sihua Liang,et al.  The existence of countably many positive solutions for nonlinear singular m-point boundary value problems on the half-line , 2008 .

[5]  D. O’Regan,et al.  Existence and uniqueness of positive solutions of boundary value problems for coupled systems of singular second-order three-point non-linear differential and difference equations , 2008 .

[6]  Z. Du,et al.  Positive solutions of M-point boundary value problem for second-order dynamic equations on time scales , 2008 .

[7]  Ismail Yaslan,et al.  Multiple positive solutions for nonlinear three-point boundary value problems on time scales , 2008, Comput. Math. Appl..

[8]  Jian-Ping Sun Twin positive solutions of nonlinear first-order boundary value problems on time scales☆ , 2008 .

[9]  Haibo Chen,et al.  Double positive solutions of boundary value problems for p-Laplacian impulsive functional dynamic equations on time scales , 2007, Comput. Math. Appl..

[10]  Douglas R. Anderson,et al.  Higher-order self-adjoint boundary-value problems on time scales , 2006 .

[11]  Ferhan Merdivenci Atici,et al.  The generalized quasilinearization method and three point boundary value problems on time scales , 2005, Appl. Math. Lett..

[12]  Wan-Tong Li,et al.  Positive solutions for nonlinear three-point boundary value problems on time scales , 2004 .

[13]  Abdelghani Ouahab,et al.  Existence results for second order boundary value problem of impulsive dynamic equations on time scales , 2004 .

[14]  Hua Luo,et al.  Existence of solutions for a two-point boundary value problem on time scales , 2004, Appl. Math. Comput..

[15]  Ravi P. Agarwal,et al.  Time scale boundary value problems on infinite intervals , 2002 .

[16]  D. Anderson Solutions to Second-order Three-point Problems on Time Scales , 2002 .

[17]  Ahmet Yantir,et al.  Positive Solutions of a Second Order m-point BVP on Time Scales , 2009 .