## 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 $$\mu$$.

### MSC:

 39A10 Additive difference equations 26D20 Other analytical inequalities
Full Text:

### References:

 [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)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.