Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 142, pp. 1-8.

Title: Long term behavior of solutions for Riccati initial-value
       problems

Authors: Sarah Y. Bahk        (California State Univ., San Bernardino, CA, USA)
         Nadejda E. Dyakevich (California State Univ., San Bernardino, CA, USA)
	 Stefan C. Johnson    (California State Univ., San Bernardino, CA, USA)

Abstract:
 The Riccati equation has been known since the early 1700s.
 Numerous papers have been written on the solvability of its
 special cases. However, to the best of our knowledge, there are no
 papers that investigate the exact (equation specific) conditions
 for unbounded growth in finite time of solutions for Riccati
 initial-value problems. In this paper, we first derive conditions
 that are necessary and sufficient for the solutions of  Riccati
 problems with constant coefficients to grow unbounded in finite
 time. Then we use a comparison method to extend these results to
 Riccati problems with variable coefficients.
 
Submitted May 23, 2008. Published October 24, 2008.
Math Subject Classifications: 34C11.
Key Words: Riccati equation; unbounded growth in finite time; comparison.