Abstract:
In this paper, by using the fixed point theorems with lattice structure, we discuss the existence of multiple solutions for the following second-point boundary value problems of dynamics equation on a general time scale.
![](https://image.hanspub.org/IMAGE/Edit_6da588a4-4c2a-4ea0-8489-1860ede74fb5.png)
(1)
where
![](https://image.hanspub.org/IMAGE/Edit_b5d6ce46-6642-4e21-a7db-6bbded026772.png)
, Let T be a closed subset of the interval[0,1] , with
![](https://image.hanspub.org/IMAGE/Edit_82093fb3-03ba-4bab-b74a-2640007e1d36.png)
, and the function
![](https://image.hanspub.org/IMAGE/Edit_c8668643-d162-4187-855b-1273d0fd6c2f.png)
is continuous, with
![](https://image.hanspub.org/IMAGE/Edit_a6ef4a7e-773f-4312-9df8-671c130cf1a4.png)
. Combining the eigenvalues of the relevant linear operator, the existence of positive, negative and sign-changing solutions is obtained under the condition that the nonlinear term is sublinear.