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:
dicbrown@bama.ua.edu DON B. HINTON Department of Mathematics, University
of Tennessee, Knoxville, TN 37996, USA. email address:
hinton@novell.math.utk.edu 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.
