Riccati techniques and oscillation for self-adjoint matrix Hamiltonian systems

Authors:
Qi-Ru Wang;Yuan-Tong Xu;Ronald M. Mathsen
Affiliations:
School of Mathematics & Computational Science, Sun Yat-Sen University, Guangzhou, Guangdong 510275, PR China;School of Mathematics & Computational Science, Sun Yat-Sen University, Guangzhou, Guangdong 510275, PR China;Department of Mathematics, North Dakota State University, Fargo, ND 58105-5075, USA
Venue:
Computers & Mathematics with Applications
Year:
2009

Citing 5
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Abstract

The purpose of this paper is to develop a generalized matrix Riccati technique for the self-adjoint matrix Hamiltonian system U^'=A(x)U+B(x)V,V^'=C(x)U-A^*(x)V. Together with the integral averaging technique and monotone functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend, improve, complement a number of existing results, and handle some cases not covered by known criteria. In particular, two interesting examples are included to illustrate the versatility of our results.