Inequalities applicable in the theory of finite difference equations. (English) Zbl 0913.39001

On nearly 9 pages there are stated 7 theorems concerning nonlinear finite difference inequalities. Some of these inequalities are used to estimate the solution of \(\Delta^2 u(t)= f(t,u(t), \mu)\) with \(u(0)=c\), \(\Delta u(0)= 0\) resp. the difference of two solutions with different \(c\) resp. different \(\mu\).


39A10 Additive difference equations
26D20 Other analytical inequalities
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[1] Agarwal, R. P., Difference Equations and Inequalities (1991), Dekker: Dekker New York
[2] Bainov, D.; Simeonov, P., Integral Inequalities and Applications (1992), Kluwer Academic: Kluwer Academic Dordrecht · Zbl 0759.26012
[3] Beesack, P. R., Gronwall Inequalities. Gronwall Inequalities, Carleton Mathematical Lecutre Notes (1975)
[4] Dragomir, S. S., On discrete generalization of Pachpatte’s inequality and applications, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), 36, 45-58 (1992) · Zbl 0804.26014
[5] Mitrinović, D. S.; Pecarić, J. E., Differential and Integral Inequalities (1988), Naucna Knjiga: Naucna Knjiga Belgrade · Zbl 0701.26010
[6] Pachpatte, B. G., Finite-difference inequalities and an extension of Lyapunov’s method, Michigan Math. J., 18, 385-391 (1971) · Zbl 0237.39001
[7] Pachpatte, B. G., On the discrete generalizations of Gronwall’s inequality, J. Indian Math. Soc., 37, 147-156 (1973) · Zbl 0331.26017
[8] Pachpatte, B. G., Finite difference inequalities and their applications, Proc. Nat. Acad. Sci. India Sect. A, 43, 348-356 (1973) · Zbl 0302.39001
[9] Pachpatte, B. G., On Bihari like integral and discrete inequalities, Soochow J. Math., 17, 213-232 (1991) · Zbl 0745.26013
[10] Pachpatte, B. G., On some new discrete inequalities related to a certain integral inequality, Libertas Math., 13, 85-97 (1993) · Zbl 0809.26010
[11] Pachpatte, B. G., Some new finite difference inequalities, Comput. Math. Appl., 28, 227-241 (1994) · Zbl 0809.26009
[12] Pachpatte, B. G., Inequalities related to a certain integral inequality arising in the theory of differential equations, Studia Univ. Babeş-Bolyai Math., 39, 33-50 (1994) · Zbl 0870.26006
[13] Pachpatte, B. G., On some new inequalities related to certain inequalities in the theory of differential equations, J. Math. Anal. Appl., 189, 128-144 (1995) · Zbl 0824.26010
[14] Pachpatte, B. G., Comparison theorems related to a certain inequality used in the theory of differential equations, Soochow J. Math., 22, 383-394 (1996) · Zbl 0867.26015
[15] Pachpatte, B. G., Inequalities similar to a certain inequality used in the theory of differential equations, Chinese J. Math., 24, 55-68 (1996) · Zbl 0899.26004
[16] Sugiyama, S., Comparison theorems on difference equations, Bull. Sci. Engrg. Res. Lab. Waseda Univ., 47, 77-82 (1970)
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