INEQUALITIES RELATED TO A CERTAIN INEQUALITY USED IN THE THEORY OF DIFFERENTIAL EQUATIONS
Main Article Content
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.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
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.