Sharp Opial-type inequalities involving $r$-derivatives and their applications

In this paper we offer very general Opial-type inequalities involving higher order r-derivatives. From these inequalities we then deduce extended and improved versions of several recent results. Some applications which dwell upon the importance of the obtained inequalities are also included.

[1]  B. G. Pachpatte.  On Opial Type Inequalities Involving Higher Order Derivatives , 1995 .

[2]  Ravi P. Agarwal,et al.  Remarks on the generalizations of Opial's inequality , 1995 .

[3]  V. Lakshmikantham,et al.  Uniqueness and nonuniqueness criteria for ordinary differential equations , 1993 .

[4]  Li Ju-Da,et al.  Opial-type integral inequalities involving several higher order derivatives , 1992 .

[5]  B. G. Pachpatte.  ON INEQUALITIES OF THE OPIAL TYPE , 1992 .

[6]  Ravi P. Agarwal,et al.  Opial's and wirtinger's type discrete inequalities in two independent variables , 1992 .

[7]  Josip Pečarić,et al.  Inequalities Involving Functions and Their Integrals and Derivatives , 1991 .

[8]  W. Cheung.  Some new Opial-type inequalities , 1990 .

[9]  B. G. Pachpatte.  On certain integral inequalities related to Opial's inequality , 1986 .

[10]  B. G. Pachpatte.  ON SOME NEW GENERALIZATIONS OF OPIAL INEQUALITY , 1986 .

[11]  C. FitzGerald.  Opial-Type Inequalities that Involve Higher Order Derivatives , 1984 .

[12]  V. A. Staikos,et al.  Correction to: Some Oscillation and Asymptotic Properties for Linear Differential Equations , 1978 .

[13]  V. A. Staikos,et al.  Non-oscillatory phenomena and damped oscillations , 1978 .

[14]  C. Philos.  Oscillatory and asymptotic behaviour of all solutions of differential equations with deviating arguments , 1978, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[15]  C. Philos,et al.  Asymptotic properties of nonoscillatory solutions of differential equations with deviating argument , 1977 .

[16]  T. Kusano,et al.  Nonoscillation theorems for differential equations with deviating argument , 1976 .

[17]  T. Kusano,et al.  Asymptotic behavior of nonoscillatory solutions of second order functional differential equations , 1975, Bulletin of the Australian Mathematical Society.

[18]  W. F. Trench.  Oscillation properties of perturbed disconjugate equations , 1975 .

[19]  D. Boyd.  Best constants in inequalities related to Opial's inequality , 1969 .

[20]  K. M. Das.  An inequality similar to Opial’s inequality , 1969 .

[21]  J. Calvert.  Some generalizations of Opial’s inequality , 1967 .