Survey on Classical Inequalities provides a study of some of the
well known inequalities in classical mathematical analysis.
Subjects dealt with include: Hardy-Littlewood-type inequalities,
Hardy's and Carleman's inequalities, Lyapunov inequalities,
Shannon's and related inequalities, generalized Shannon functional
inequality, operator inequalities associated with Jensen's
inequality, weighted Lp -norm inequalities in convolutions,
inequalities for polynomial zeros as well as applications in a
number of problems of pure and applied mathematics. It is my
pleasure to express my appreciation to the distinguished
mathematicians who contributed to this volume. Finally, we wish to
acknowledge the superb assistance provided by the staff of Kluwer
Academic Publishers. June 2000 Themistocles M. Rassias Vll LYAPUNOV
INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of
Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA.
email address:
[email protected] DON B. HINTON Department of
Mathematics, University of Tennessee, Knoxville, TN 37996, USA.
email address:
[email protected] Abstract. For nearly 50
years Lyapunov inequalities have been an important tool in the
study of differential equations. In this survey, building on an
excellent 1991 historical survey by Cheng, we sketch some new
developments in the theory of Lyapunov inequalities and present
some recent disconjugacy results relating to second and higher
order differential equations as well as Hamiltonian systems. 1.
Introduction Lyapunov's inequality has proved useful in the study
of spectral properties of ordinary differential equations. Typical
applications include bounds for eigenvalues, stability criteria for
periodic differential equations, and estimates for intervals of
disconjugacy.
General
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