Asymptotic theory for a critical class of third-order differential equations

Asymptotic theory for a critical class of third-order differential equations

An asymptotic theory is developed for a class of third-order differential equations. We identify a critical case to obtain the asymptotic form of three linearly independent solutions for large x.

___

  • [1] Al-Hammadi ASA. Asymptotic theory for third-order differential equations. Mathematika 1988; 35: 225-232.
  • [2] Al-Hammadi ASA. Asymptotic theory for third-order differential equation of Euler type. Results in Mathematics 1990; 17: 1-14.
  • [3] Al-Hammadi ASA. Asymptotic theory for third-order differential equations with extension to higher odd-order equations. Proceedings of the Royal Society of Edinburgh 1991; 117A: 215-223.
  • [4] Eastham MSP. Asymptotic theory for a critical class of fourth-order differential equations. Proceedings of the Royal Society London 1982; A383: 173-188.
  • [5] Eastham MSP. The asymptotic solution of linear differential systems. Mathematika 1985; 32: 131-138.
  • [6] Eastham MSP. The Asymptotic Solution of Linear Differential Systems: Applications of Levinson Theorem. Oxford, UK: Clarendon Press, 1989.
  • [7] Eastham MSP. A repeated transformation in the asymptotic solution of linear differential systems. Proceedings of the Royal Society of Edinburgh 1986; 102A: 173-397.
  • [8] Everitt WN, Zettl A. Generalized symmetric ordinary differential expressions I: the general theory. Nieuw Archief voor Wiskunde 1979; 27: 363-397.
  • [9] Pfeiffer GW. Asymptotic solutions of y ′′′ + qy′ + ry = 0. Journal of Differential Equations 1972; 11: 145-155.
  • [10] Unsworth K. Asymptotic expansions and deficiency indices associated with third-order self-adjoint differential operators. The Quarterly Journal of Mathematics 1973; 24 (1): 177-188.