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Willett, D.; Wong, J. S. W.

On the discrete analogues of some generalizations of Gronwall’s inequality. (English) Zbl 0145.06003

Monatsh. Math. 69, 362-367 (1965).
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Cited in 3 Reviews
Cited in 67 Documents

Keywords:

differentiation and integration, measure theory
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References:

[1] T. H. Gronwall, ?Note on the derivatives with respect to a parameter of the solutions of a system of differential equations?, Ann. of Math.,20 (1918), 292-296. · JFM 47.0399.02 · doi:10.2307/1967124
[2] I. Bihari, ?A generalization of a lemma of Bellman and its applications to uniqueness problems of differential equations?, Acta Math. Acad. Sci. Hungary7 (1956), 81-94. · Zbl 0070.08201 · doi:10.1007/BF02022967
[3] C. E. Langenhop, ?Bounds on the norm of a solution of a general differential equation?, Proc. Amer. Math. Soc.11 (1960), 795-799.
[4] V. Lakshmikantham, ?Upper and lower bounds of the norm of solutions of differential equations,? Proc. Amer. Math. Soc.13 (1962), 615-616. · Zbl 0107.28801 · doi:10.1090/S0002-9939-1962-0137878-1
[5] F. Brauer, ?Bounds for solutions of ordinary differential equations?, Proc. Amer. Math. Soc.14 (1963), 36-43. · Zbl 0113.06803 · doi:10.1090/S0002-9939-1963-0142829-0
[6] V. Lakshmikantham, ?Upper and lower bounds of the norm of solutions of differential systems?, Proc. Amer. Math. Soc.14 (1963), 509-513. · Zbl 0117.05302 · doi:10.1090/S0002-9939-1963-0148997-9
[7] D. Willett, ?Nonlinear vector integral equations as contraction mappings?, Archive for Rat. Mech. and Analysis,15 (1964), 79-86. · Zbl 0161.31902
[8] T. E. Hull andW. A. J. Luxemburg, ?Numerical methods and existence theorems for ordinary differential equations?, Numerische Math.2 (1960), 30-41. · Zbl 0089.29003 · doi:10.1007/BF01386206
[9] Yue-sheng Li, ?The bound, stability and error estimates for the solution of nonlinear differential equations?, Chinese Math. (A. M. S. Translation)3 (1963), 34-41.
[10] M. Lees, ?Energy inequalities for the solution of differential equations?, Trans. Amer. Math. Soc.94 (1960), 58-73. · Zbl 0104.34903 · doi:10.1090/S0002-9947-1960-0114045-1
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