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Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order

In: Theory of Third-Order Differential Equations

Author

Listed:
  • Seshadev Padhi

    (Birla Institute of Technology, Mesra, Department of Applied Mathematics)

  • Smita Pati

    (Birla Institute of Technology, Mesra, Department of Applied Mathematics)

Abstract

This chapter is concerned with the study of oscillatory and asymptotic behaviour of nonoscillatory solutions of nonhomogeneous third-order differential equations of the form $$x^{\prime\prime\prime} + a(t) x^{\prime\prime} + b(t)x^{\prime} + c(t) x = f \bigl(t,x,x^{\prime},x^{\prime\prime}\bigr), $$ where a, b and c∈C([σ,∞),R) and f:[σ,∞)×R 3→R, σ∈R. z-type oscillation criteria has been used in this chapter to study the nonoscillation of solutions of the considered equation. As an application, some sufficient conditions have been given for the nonoscillation of different mathematical models in Engineering.

Suggested Citation

  • Seshadev Padhi & Smita Pati, 2014. "Oscillation and Nonoscillation of Nonlinear Nonhomogeneous Differential Equations of Third Order," Springer Books, in: Theory of Third-Order Differential Equations, edition 127, chapter 0, pages 305-334, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1614-8_5
    DOI: 10.1007/978-81-322-1614-8_5
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