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. We investigate the stability of nonlinear dierential equa-tions of the form y (n) (x) = F(x,y(x),y ′ (x),...,y (n−1) (x)) with a Lips-chitz condition by using a xed point method. Moreover, a Hyers-Ulamconstant of this dierential equation is obtained. 1. Introduction and preliminariesIn 1940, S. M. Ulam [49] posed the following question concerning the stabilityof group homomorphisms before a Mathematical Colloquium: When can weassert that the solutions of an inequality are close to one of the exact solutionsof the corresponding equation?A year later, D. H. Hyers [15] dealt with e-additive mapping by directmethod, which gave a partial solution to the above question. The result wasextended by T. Aoki [2], D. G. Bourgin [4] and Th. M. Rassias [40]. We men-tion here that the interest of this topic has been increasing since it came intobeing, some other results concerning functional equations one can nd, e.g., in[9, 10, 11, 19, 37, 42, 43] and some related information (e.g., e-isometries, su-perstability of functional equations and the stability of dierential expressions)we refer to [3, 5, 6, 8, 14, 16, 17, 18, 36, 47].To the best of our knowledge, the rst one who pay attention to the sta-bility of dierential equations is M. Oblo za [34, 35]. Thereafter, C. Alsinaand R. Ger [1] proved that the stability holds true for dierential equationy

ON HYERS-ULAM STABILITY OF NONLINEAR DIFFERENTIAL EQUATIONS