Oscillate Criteria of a Class of Higher Order Linear Functional Equations

On the hyper order of solutions of a class of higher order linear differential equations

In this paper, we investigate the order and the hyper order of entire solutions of the higher order linear differential equation f +Ak−1 (z) e k−1f +...+A1 (z) e 1f ′ +A0 (z) e 0f = 0 (k ≥ 2) , where Pj (z) (j = 0, ..., k − 1) are nonconstant polynomials such that degPj = n (j = 0, ..., k − 1) and Aj (z) ( ≡ 0) (j = 0, ..., k − 1) are entire functions with ρ (Aj) < n (j = 0, ..., k − 1). Under ...

Finite and Infinite Order Solutions of a Class of Higher Order Linear Differential Equations

In this paper, we investigate the growth of solutions of higher order linear differential equations where most of the coefficients have the same order and type with each other.

Dynamics of a Class of Higher Order Difference Equations

Linearizability Criteria for a Class of Third Order Semi-Linear Ordinary Differential Equations

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a class of third order semi-linear ordinary differential equations, which is distinct from the classes available in the literature. Some examples are given and...

Oscillation Criteria for a Class of Functional Parabolic Equations

Oscillations of parabolic equations with functional arguments are studied, and sufficient conditions are derived for all solutions of certain boundary value problems to be oscillatory in a cylindrical domain. Our approach is to reduce the multi-dimensional problems to one-dimensional problems for functional differential inequalities.