Oscillation criteria for extended linear matrix Hamiltonian systems
G. A. Grigorian
TL;DR
This paper develops new oscillation criteria for extended linear matrix Hamiltonian systems using the Riccati equation method, notably relaxing the positive definiteness condition on coefficients, and compares these results with existing ones.
Contribution
It introduces a novel approach to oscillation criteria that removes the positive definiteness restriction on system coefficients.
Findings
New oscillation criteria established
Comparison with existing results demonstrates improvements
Examples illustrate the applicability of the criteria
Abstract
The Riccati equation method is used to establish new oscillation criteria for extended linear matrix Hamiltonian systems. This method allows to obtain results in in a new direction, which is to break the positive definiteness condition, imposed on one of coefficients of the system. Some examples are provided for comparing the obtained results with each other and with the result of K. I. Al - Dosary, H. Kh. Abdullah and D. Husein.
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Taxonomy
TopicsMatrix Theory and Algorithms · Numerical methods for differential equations · Spectral Theory in Mathematical Physics