Solvability for a third-order three-point BVP on time scales

We are concerned with the existence of a nontrivial solution to a nonlinear third-order three-point boundary-value problem on general time scales. Using the corresponding Green function, without a non-negative or monotone-type assumption on the nonlinearity, we obtain sufficient conditions for the existence of at least one nontrivial solution, using the Leray-Schauder nonlinear alternative theorem. This paper extends recent results in differential equations to difference equations, quantum equations, and general dynamic equations on time scales.

[1]  Shuhong Li,et al.  Positive solutions of nonlinear singular third-order two-point boundary value problem , 2006 .

[2]  D. Anderson,et al.  THIRD-ORDER NONLOCAL PROBLEMS WITH SIGN-CHANGING NONLINEARITY ON TIME SCALES , 2007 .

[3]  D. Anderson,et al.  Twin monotone positive solutions to a singular nonlinear third-order differential equation , 2007 .

[4]  Positive Solutions of a Nonlinear Third Order Eigenvalue Problem , 2006 .

[5]  M. Pei,et al.  Existence and uniqueness of solutions for third-order nonlinear boundary value problems☆ , 2007 .

[6]  A. Cabada,et al.  Third-order right-focal multi-point problems on time scales , 2006 .

[7]  K. Deimling.  Nonlinear functional analysis , 1985 .

[8]  G. Guseinov,et al.  On Green's functions and positive solutions for boundary value problems on time scales , 2002 .

[9]  Wu,et al.  Positive Solutions to a Singular Third-Order Three-Point Boundary Value Problem , 2009 .

[10]  D. Anderson,et al.  EXISTENCE OF SOLUTIONS TO A THIRD-ORDER MULTI-POINT PROBLEM ON TIME SCALES , 2007 .

[11]  A. Palamides,et al.  Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green’s function , 2008 .

[12]  Jian-Ping Sun,et al.  Existence of solution and positive solution of BVP for nonlinear third-order dynamic equation , 2006 .

[13]  Noel G. Lloyd,et al.  CENTRES AND LIMIT CYCLES FOR AN EXTENDED KUKLES SYSTEM , 2007 .

[14]  Yongping Sun,et al.  Positive solutions of singular third-order three-point boundary value problem ✩ , 2005 .

[15]  D. Anderson,et al.  q-Dominant and q-recessive matrix solutions for linear quantum systems , 2007 .

[16]  Jian-Ping Sun,et al.  Existence of positive solutions for nonlinear third-order three-point boundary value problems☆ , 2008 .

[17]  S. Kang,et al.  Positive solutions of a singular nonlinear third order two-point boundary value problem , 2007 .

[18]  N. Kosmatov,et al.  Third-order boundary value problems with sign-changing solutions , 2007 .

[19]  Xinguang Zhang,et al.  Positive solutions of second-order m-point boundary value problems with changing sign singular nonlinearity , 2007, Appl. Math. Lett..