Nonoscillation of second-order nonhomogeneous differential equations

Oscillation and Nonoscillation Criteria for Second-order Linear Differential Equations

Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established. 1. Statement of the Problem and Formulation of Basic Results Consider the differential equation u′′ + p(t)u = 0, (1) where p : [0, +∞[→ [0, +∞[ is an integrable function. By a solution of equation (1) is understood a function u : [0,+∞[→] − ∞, +∞[ which is locally absolutely continuous tog...

Nonoscillation criteria for second-order nonlinear differential equations

Consider the second order nonlinear differential equations with damping term and oscillation’s nature of ( ( ) '( )) ' ( ) '( ) ( ) ( ( )) ( '( )) 0 r t x t p t x t q t f x t k x t    0 t t  (1) to used oscillatory solutions of differential equations ( ( ) '( )) ' ( ) ( ( )) ( '( )) 0 t x t t f x t k x t     (2) where ( ) t  and ( ) t  satisfy conditions given in this work paper. Our ...

On Second-Order Differential Equations with Nonhomogeneous -Laplacian

Oscillation and Nonoscillation of Forced Second Order Dynamic Equations

Oscillation and nonoscillation properties of second order Sturm–Liouville dynamic equations on time scales attracted much interest. These equations include, as special cases, second order self-adjoint differential equations as well as second order Sturm–Liouville difference equations. In this paper we consider a given (homogeneous) equation and a corresponding equation with forcing term. We giv...

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