Oscillation with respect to partial variables of linear second-order differential systems

Authors:
Zong Qi Deng and Shi Gui Ruan

Journal:
Proc. Amer. Math. Soc. **113** (1991), 777-783

MSC:
Primary 34C10

MathSciNet review:
1070514

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Consider the second-order vector differential system (1) and matrix differential system (2) , where is an -dimensional vector function and and are continuous matrix functions. In this article, we establish the concept that systems (1) and (2) are oscillatory with respect to partial variables. Some sufficient conditions are obtained; several examples are given to illustrate the results.

**[1]**Shair Ahmad,*On positivity of solutions and conjugate points of nonselfadjoint systems*, Bull. Acad. Polon. Sci. Sér. Sci. Math.**27**(1979), no. 1, 71–75 (English, with Russian summary). MR**539335****[2]**Shair Ahmad and Alan C. Lazer,*A new generalization of the Sturm comparison theorem to selfadjoint systems*, Proc. Amer. Math. Soc.**68**(1978), no. 2, 185–188. MR**0470327**, 10.1090/S0002-9939-1978-0470327-4**[3]**Shair Ahmad and C. C. Travis,*Oscillation criteria for second-order differential systems*, Proc. Amer. Math. Soc.**71**(1978), no. 2, 247–252. MR**0486792**, 10.1090/S0002-9939-1978-0486792-2**[4]**F. V. Atkinson, Hans G. Kaper, and Man Kam Kwong,*An oscillation criterion for linear second-order differential systems*, Proc. Amer. Math. Soc.**94**(1985), no. 1, 91–96. MR**781063**, 10.1090/S0002-9939-1985-0781063-2**[5]**Richard Bellman,*Introduction to matrix analysis*, Second edition, McGraw-Hill Book Co., New York-Düsseldorf-London, 1970 (Russian). MR**0258847****[6]**G. J. Butler, L. H. Erbe, and A. B. Mingarelli,*Riccati techniques and variational principles in oscillation theory for linear systems*, Trans. Amer. Math. Soc.**303**(1987), no. 1, 263–282. MR**896022**, 10.1090/S0002-9947-1987-0896022-5**[7]**Philip Hartman,*Ordinary differential equations*, 2nd ed., Birkhäuser, Boston, Mass., 1982. MR**658490****[8]**W. J. Kim,*Comparison theorems for second order differential systems*, Proc. Amer. Math. Soc.**96**(1986), no. 2, 287–293. MR**818460**, 10.1090/S0002-9939-1986-0818460-3**[9 M]**Man Kam Kwong, Hans G. Kaper, Kazuo Akiyama, and Angelo B. Mingarelli,*Oscillation of linear second-order differential systems*, Proc. Amer. Math. Soc.**91**(1984), no. 1, 85–91. MR**735570**, 10.1090/S0002-9939-1984-0735570-8**[10]**Angelo B. Mingarelli,*On a conjecture for oscillation of second-order ordinary differential systems*, Proc. Amer. Math. Soc.**82**(1981), no. 4, 593–598. MR**614884**, 10.1090/S0002-9939-1981-0614884-3**[11]**Shi Gui Ruan and Zong Qi Deng,*Oscillation of second-order linear differential systems*, J. Central China Normal Univ. Natur. Sci.**24**(1990), no. 1, 1–6 (Chinese, with English summary). MR**1072700**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
34C10

Retrieve articles in all journals with MSC: 34C10

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1070514-7

Keywords:
Oscillation with respect to partial variable,
prepared solutions,
secondorder differential systems

Article copyright:
© Copyright 1991
American Mathematical Society