INEQUALITIES RELATED TO A CERTAIN INEQUALITY USED IN THE THEORY OF DIFFERENTIAL EQUATIONS

Authors

  • B. G. PACHPATTE Department of Marathematics, Marathwa心 Uuiversity, Aurangahad 431 004, (Maharashtra) India.

DOI:

https://doi.org/10.5556/j.tkjm.29.1998.4240

Keywords:

Inequalities, theory of differential equations, sum-difference equations, submultiplicative, bounds on the solutions

Abstract

In this paper we establish some new integral and finite difference inequalities related to a certain integral inequality used in the theory of differential equations. The inequalities obtained here can be used as handy tools in the theory of some new classes of integralral and sum-difference equations.

References

V. Barbu, Differential Equations, Ed. Junimea, Iasi, 1985. [In Romanian]

F. Brauer, The use of comparison theorems for ordinary differential equations, Stability problems of solutions of differential equations, Proc. of NATO Advanced Study Institute, Padua, Italy, 1965, 29-50

C. M. Dafermos, The second law of theomodynamics and stability, Arch. Rational Mech. Anal., 70(1979), 167-179.

S. S. Dragomir, The Gronwall type Lemmas and Applications, Monogrfii Mathmatice, Univ. Timisoarn, 29, 1987.

A. Haraux, Nonlinear Evolution Equations : Global Behavior of solutions, Lecture Note in Mathematics, Springer-Verlag, Berlin, New York 841, 1981.

D. S. Mitrinovic and J. L. Pecaric, Differential and lntegral Inequalities, Naucna Knjiga Belgrade, 1988.

S. N. Olekhnik, Boundedness and unboundedness of solutions of some systems of ordinary differential equations," Vestnik Moskov. Univ. Mat., 27(1972), 34-44.

L. Ou-Iang, The boundedness of solutions of linear differenctial equations $y''+A(t)y =0$, Shuxue Jinzhan 3(1957), 409-415.

B. G. Pachpattc, Finite-difference inequalities and an extension of Lyapunov's method, Michigan Math. J., 18(1971), 385-391.

B. G. Pachpatte, On the discrete generalizations of Gronwall's inequality, J. Indian Math Soc., 37(1973), 147-156.

B. G. Pachpattc, On a certain inequality arising in the theory of differential equations, J. Math. Anal. Appl., 182(1994), 143-157.

B. G. Pachpatte, Some new finite difference inequalities, Computers Math. Applic., 28 (1994), 227-273.

B. G. Pachpatte, On some fundamental integral inequalities arising in the theory of differential equations, Cninese J. Math. 22(1994), 261-273.

B. G. Pachpattc, On some new inequalities related to certain inequalities in the theory of differential equations, J. Math. Anal. Appl., 189(1995), 128-144.

M. Tsutsum1and I. Fukunda, On solutions of the derivative nonlinear Schrodinger equation: Existence and uniqueness theorem, Funkcial. Ekvac., 23(1980), 259-277.

W. Walter, Differential and Integral Inequalities Springer-Verlag, Berlin, New York, 1970.

Downloads

Published

1998-03-01

How to Cite

PACHPATTE, B. G. (1998). INEQUALITIES RELATED TO A CERTAIN INEQUALITY USED IN THE THEORY OF DIFFERENTIAL EQUATIONS. Tamkang Journal of Mathematics, 29(1), 1-11. https://doi.org/10.5556/j.tkjm.29.1998.4240

Issue

Section

Papers