Oscillation of two-dimensional linear second-order differential systems

Journal Article · Fri Feb 01 00:00:00 EST 1985 · J. Differ. Equations; (United States)

DOI:https://doi.org/10.1016/0022-0396(85)90104-4· OSTI ID:6700380

Kwong, M K; Kaper, H G

This article is concerned with the oscillatory behavior at infinity of the solution y: (a, infinity) ..-->.. R/sup 2/ of a system of two second-order differential equations, y''(t) + Q(t) y(t) = 0, t epsilon(a, infinity); Q is a continuous matrix-valued function on (a, infinity) whose values are real symmetric matrices of order 2. It is shown that the solution is oscillatory at infinity if the largest eigenvalue of the matrix integral/sub a//sup t/ Q(s) ds tends to infinity as t ..-->.. infinity. This proves a conjecture of D. Hinton and R.T. Lewis for the two-dimensional case. Furthermore, it is shown that considerably weaker forms of the condition still suffice for oscillatory behavior at infinity. 7 references.

• Research Organization: Argonne National Lab., IL
• DOE Contract Number: W-31-109-ENG-38
• OSTI ID: 6700380
• Journal Information: J. Differ. Equations; (United States), Vol. 56:2
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
DIFFERENTIAL EQUATIONS
ANALYTICAL SOLUTION
EIGENVALUES
LIMITING VALUES
MATRICES
OSCILLATIONS
TWO-DIMENSIONAL CALCULATIONS
EQUATIONS
990230* - Mathematics & Mathematical Models- (1987-1989)