Journal of Inequalities and Applications 
Volume 5 (2000), Issue 1, Pages 11-37
doi:10.1155/S1025583400000023

Some opial, Lyapunov, and De IaValée poussin inequalities with nonhomogeneous boundary conditions

Richard C. Brown,1 A. M. Fink,2 and Don B. Hinton3

 1Department of Mathematics, University of Alabama, Tuscaloosa 35487-0350, AL, USA
2Department of Mathematics, Iowa State University, Ames 50011, IA, USA
3Department of Mathematics, University of Tennessee, Knoxville 37996, TN , USA
Received 18 January 1999; Revised 30 January 1999

Abstract

We derive Opial-type inequalities for a class of real functions satisfying nonhomogenous boundary conditions and determine the best constant and extremals. The results are then used to obtain generalized Lyapunov and De la Valée Poussin inequalities.