Higher-order three-point boundary value problem on time scales

In this paper, we consider a higher-order three-point boundary value problem on time scales. We study the existence of solutions of a non-eigenvalue problem and of at least one positive solution of an eigenvalue problem. Later we establish the criteria for the existence of at least two positive solutions of a non-eigenvalue problem. Examples are also included to illustrate our results.

[1]  A. Peterson,et al.  Three Point Boundary Value Problems on Time Scales , 2004 .

[2]  Douglas R. Anderson,et al.  NONLINEAR TRIPLE-POINT PROBLEMS ON TIME SCALES , 2004 .

[3]  D. Anderson,et al.  An even-order three-point boundary value problem on time scales , 2004 .

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

[5]  Erbil Çetin,et al.  Higher order boundary value problems on time scales , 2007 .

[6]  Johnny Henderson,et al.  Multiple solutions for 2mth-order Sturm-Liouville boundary value problems , 2000 .

[7]  C. Chyan Eigenvalue Intervals for 2mth Order Sturm—Liouville Boundary Value Problems , 2002 .

[8]  E. Kaufmann,et al.  POSITIVE SOLUTIONS OF A THREE-POINT BOUNDARY-VALUE PROBLEM ON A TIME SCALE , 2003 .

[9]  R. Ma,et al.  Positive solutions of a nonlinear three-point boundary-value problem. , 1999 .

[10]  Eigenvalue problems for a three-point boundary-value problem on a time scale , 2004 .

[11]  Allan Peterson,et al.  Three positive fixed points of nonlinear operators on ordered banach spaces , 2001 .

[12]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .

[13]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

[14]  E. Berchio,et al.  ftp ejde.math.txstate.edu (login: ftp) SOME REMARKS ON BIHARMONIC ELLIPTIC PROBLEMS WITH POSITIVE, INCREASING AND CONVEX NONLINEARITIES , 2022 .

[15]  Leo F. Boron,et al.  Positive solutions of operator equations , 1964 .

[16]  R. Ma,et al.  Positive Solutions of Three-point Nonlinear Discrete Second Order Boundary Value Problem , 2004 .

[17]  John M. Davis,et al.  Existence results for singular three point boundary value problems on time scales , 2004 .

[18]  Hua Luo,et al.  POSITIVE SOLUTIONS TO A GENERALIZED SECOND-ORDER THREE-POINT BOUNDARY-VALUE PROBLEM ON TIME SCALES , 2005 .

[19]  Bing Liu Positive solutions of a nonlinear three-point boundary value problem , 2002, Appl. Math. Comput..

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

[21]  K. R. Prasad,et al.  Comparison of eigenvalues for lidstone boundary value problems on a measure chain (preprint) , 1999 .