Adil Misir

More on the explicit solutions for a second-order nonlinear boundary value problem

The explicit solutions to the boundary value problem x″(t)=λ(t)eμ(t)x(t) x(0)=x(1)=0, where λ and μ are continuous functions, are discussed.

Oscillation and nonoscillation of half-linear Euler type differential equations with different periodic coefficients

Abstract In this paper, we compute explicitly the oscillation constant for certain half-linear second-order differential equations having different periodic coefficients. Our result covers known result concerning half-linear Euler type differential equations with α—periodic positive coefficients. Additionally, our result is new and original in case that the least common multiple of these periods is not defined. We give an example and corollaries which illustrate cases that are solved with our result.

Asymptotic iteration technique for second-order dynamic equations on time scales

An asymptotic iteration method for solving second-order homogeneous linear dynamic equation of the form y△△ = a0(t)y△ + b0(t)y is introduced. Where a0(t) and b0(t) are Crdm(T) functions and the positive integer m depends on the differentiability of a0(t), b0(t) and iteration steps.

Reducibility and Stability Results for Linear System of Difference Equations

We first give a theorem on the reducibility of linear system of difference equations of the form . Next, by the means of Floquet theory, we obtain some stability results. Moreover, some examples are given to illustrate the importance of the results.

Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients

We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.