On the Asymptotic Behavior of Solutions of Certain Third-order Nonlinear Differential Equations

  title={On the Asymptotic Behavior of Solutions of Certain Third-order Nonlinear Differential Equations},
  author={Cemil Tunç},
where ψ ∈ C(R×R×R,R), f ∈ C(R×R,R), and p ∈ C([0,∞)×R×R×R,R). It is also supposed that the functions ψ, f , and p depend only on the arguments displayed explicitly, and the dots denote differentiation with respect to t. However, we shall require that f (0,0) = 0, the derivatives ∂ψ(x, ẋ, ẍ)/∂x ≡ ψx(x, ẋ, ẍ), ∂ψ(x, ẋ, ẍ)/∂ẍ ≡ ψẍ(x, ẋ, ẍ), and ∂ f (x, ẋ)/∂x ≡ fx(x, ẋ) exist and are continuous, and the uniqueness of the solutions of (1.1) will be assumed. In relevant literature, a good deal of… CONTINUE READING

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