Stability problem for the composite type functional equations

Oscillation Theorems for Nonlinear Differential Equations of Fourth-Order

“…We aim for a solution of Equation (1) or Equation (2) as a function x(t) : [t x , ∞) → R, t x ≥ t 0 such that x(t) and r (t) (x (t)) α are continuously differentiable for all t ∈ [t x , ∞) and sup{|x(t)| : t ≥ T} > 0 for any T ≥ t x . We assume that Equation (1) or Equation (2) possesses such a solution. A solution of Equation (1) or Equation 2is called oscillatory if it has arbitrarily large zeros on [t x ‚ ∞).…”