Behavior of solutions of linear second order differential equations

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

The behavior of solutions of second order delay differential equations

In this paper, we study the behavior of solutions of second order delay differential equation y′′(t)= p1y′(t)+ p2y′(t − τ )+ q1y(t)+ q2y(t − τ ), where p1, p2, q1, q2 are real numbers, τ is positive real number. A basic theorem on the behavior of solutions is established. As a consequence of this theorem, a stability criterion is obtained. © 2006 Elsevier Inc. All rights reserved.

Behavior of Solutions of Second Order Self- Adjoint Differential Equations

Nonrectifiable Oscillatory Solutions of Second Order Linear Differential Equations

The second order linear differential equation (p(x)y′)′ + q(x)y = 0 , x ∈ (0, x0] is considered, where p, q ∈ C1(0, x0], p(x) > 0, q(x) > 0 for x ∈ (0, x0]. Sufficient conditions are established for every nontrivial solutions to be nonrectifiable oscillatory near x = 0 without the Hartman–Wintner condition.

On Approximate Solutions of Second-Order Linear Partial Differential Equations

In this paper, a Chebyshev polynomial approximation for the solution of second-order partial differential equations with two variables and variable coefficients is given. Also, Chebyshev matrix is introduced. This method is based on taking the truncated Chebyshev expansions of the functions in the partial differential equations. Hence, the result matrix equation can be solved and approximate va...