Existence Of Solutions For Several Nonlinear Two-Point Boundary Value Problems On Time Scales

The paper is concerned with existence of solutions to four two-point boundary value problems of differential equation on time scales. The main results are as follows:1. Under the existence of barrier strips, the existence theorem is established for the following boundary value problem on time scales by using properties of derivative on time scales.Meanwhile, the corresponding existence theorem is presented for the followingiboundary value problem on time scales2. Suppose there exist some special barrier strips. We come up with a new concept-scatter degree, and obtain the existence theorem for the fo-llowing boundary value problem on time scales by using induction principle on time scales.Similarly, the corresponding existence result is founded for the following boundary value problem on time scales by using the induction principle of duality on time scales.These theorems are achieved without any growth restrictions on the nonlinear arguments f and g. Our results extend the existence theorems which have gained for two-point boundary value problems of ordinary differential equation by P. Kelevedjiev in 1994.