General Letters in Mathematic, Vol. 3, No.1, Oct 2017, pp. 57-70 e-ISSN 2519-9277, p-ISSN 2519-9269 Available online at http:\\ www.refaad.com Hyers-Ulam-Rassias Stability Criteria of Nonlinear Differential Equations of Lane-Emden Type Maher Nazmi Qarawani Department of Mathematics, Al-Quds Open University, Salfit, West-Bank, Palestine mkerawani@qou.edu Abstract In this paper we establish Hyers-Ulam-Rassias stability and Hyers-Ulam Criteria for second order non-linear ordinary differential equations of Lane-Emden type; moreover two examples of such equations are considered. Keywords: Hyers-Ulam-Rassias Stability, Nonlinear Differential Equations, Lane-Emden Type. MSC: 34Cxx , 34K20, 37C75. 1 Introduction Equations of the Lane-Emden type arise in mathematical physics and astrophysics. These Equations describe the temperature variations of a spherical gas cloud under the mutual attraction of its molecules and subject to the law of classical thermodynamics, [17]. The objective of this article is to investigate the Hyers-Ulam-Rassias Stability for the Lane-Emden type equation   1 () ()() () n u t u gtfu ht t       (1.1) and the nonlinear differential equation of second order   1 () ()() 0 n u t u gtfu t       (12) with the initial conditions. 0 0 0 1 ( ) , ( ) ut u ut u    (1.3) Moreover in this paper we consider the Hyers-Ulam-Rassias Stability for the Emden-Fowler equation   2 () ()() 0 u t u gtfu t      (1.4) Here n is a real parameter such that 2 n  , 0 [ , ], t t T  0 0 t T    , ( ) : [0, ) , ( ) : [0, ) ht Rgt R   are continuous. Suppose that there is 0 L  such that ( ( )) ( ( )) fut fvt Lu v    (1.5) In 1940, Ulam [27] posed the stability problem of functional equations. In the talk, Ulam