S. Gulsan Topal

The generalized quasilinearization method and three point boundary value problems on time scales

In this paper, we study the convergence of monotone sequences of iterates for nonlinear second order dynamic equations with three point boundary conditions on time scales. We prove that it is possible to construct two sequences converging to the unique solution of the three point boundary value problem from above and below with high rate of convergence.

Existence of multiple positive solutions for the system of higher order boundary value problems on time scales

In this paper, by applying fixed point theorems in cones and under suitable conditions, we present the existence of single and multiple solutions for system of higher order boundary value problems on time scales.

Existence of positive solutions of a Sturm-Liouville BVP on an unbounded time scale

A fixed point theorem of Guo-Krasnoselskii type is used to establish existence results for the nonlinear Sturm-Liouville dynamic equation with the boundary conditions on an unbounded time scale. Later on the positivity and the boundedness of the solutions are obtained by imposing some conditions on f.

Rolle's and Generalized Mean Value Theorems on Time Scales

In this paper, some basic rules of calculus on R are presented for arbitrary time scales. This allows us to prove Rolles and mean value theorems on a time scale.

Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales

We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.