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Oscillation of Solutions of Linear 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

Linear nonhomogeneous differential equations of the form 3.1 $$ x^{\prime\prime\prime}+a(t)x^{\prime\prime}+b(t)x^{\prime}+c(t)x=f(t), $$ where a,b∈C 1([σ,∞),R) and c∈C([σ,∞),R), has been considered in Chap. 3. Existence of oscillatory solutions of the equation has been given in this chapter for the cases (i) a(t)≥0, b(t)≤0, c(t)>0, (ii) a(t)≤0, b(t)≤0, c(t)>0, and (iii) a(t)≥0, b(t)≥0, c(t)>0. Rest cases have been left as an open problem. Further, Green’s function method has been given in this chapter so that all oscillatory solutions of a linear nonhomogeneous differential equation of the form (7.65) tends to zero eventually.

Suggested Citation

  • Seshadev Padhi & Smita Pati, 2014. "Oscillation of Solutions of Linear Nonhomogeneous Differential Equations of Third Order," Springer Books, in: Theory of Third-Order Differential Equations, edition 127, chapter 0, pages 147-191, Springer.
    • Handle: RePEc:spr:sprchp:978-81-322-1614-8_3
    DOI: 10.1007/978-81-322-1614-8_3
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