Sarah Y. Bahk, Nadejda E. Dyakevich, Stefan C. Johnson
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.
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Sarah Y. Bahk 5500 University Parkway, San Bernardino, CA 92407-2397, USA email: sbahk@csusb.edu |
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Nadejda E. Dyakevich Department of Mathematics California State University San Bernardino 5500 University Parkway, San Bernardino, CA 92407-2397, USA email: dyakevic@csusb.edu |
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Stefan C. Johnson Department of Mathematics California State University San Bernardino 5500 University Parkway, San Bernardino, CA 92407-2397, USA email: steve@sevej.us |
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