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

Survey on Classical Inequalities (Mathematics and Its Applications Book 517) PDF

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