This paper studies the radial symmetry of positive solutions of nonlinear elliptic equations in $ \mathbb{R}^n $. The main result, Theorem 1, states that under the condition that $ f'(s) \leq 0 $ for sufficiently small $ s > 0 $, all positive solutions of the equation $ \Delta u + f(u) = 0 $ in $ \mathbb{R}^n $ with $ \lim_{|x| \to \infty} u(x) = 0 $ must be radially symmetric about the origin (up to translation) and satisfy $ u_r < 0 $ for $ r = |x| > 0 $. The paper also presents Theorem 2, which generalizes Theorem 1 to fully nonlinear equations of the form $ F[u] = 0 $, where $ F $ satisfies certain conditions. The proof of Theorem 2 relies on the method of moving planes and the maximum principle. The key idea is that the usual maximum principle can be applied to handle the difficulties that might arise in getting the moving plane device started near infinity. The paper also discusses related results, including Theorem A by Gidas, Ni, and Nirenberg, which establishes radial symmetry for solutions of the scalar field equation $ \Delta u - u + u^p = 0 $ in $ \mathbb{R}^n $, and Theorem B by Franchi and Lanconelli, which extends the result to quasilinear equations. Additionally, C. Li extends the result to fully nonlinear equations. The paper also provides an example showing that solutions can decay at infinity slower than logarithmic decay, and another example demonstrating that the symmetric point does not necessarily have to be the origin if the equation depends on $ |x| $. The main contribution of the paper is the proof of Theorem 2, which shows that under certain conditions, all positive solutions of the fully nonlinear equation are radially symmetric about some point in $ \mathbb{R}^n $ and strictly decreasing away from that point.This paper studies the radial symmetry of positive solutions of nonlinear elliptic equations in $ \mathbb{R}^n $. The main result, Theorem 1, states that under the condition that $ f'(s) \leq 0 $ for sufficiently small $ s > 0 $, all positive solutions of the equation $ \Delta u + f(u) = 0 $ in $ \mathbb{R}^n $ with $ \lim_{|x| \to \infty} u(x) = 0 $ must be radially symmetric about the origin (up to translation) and satisfy $ u_r < 0 $ for $ r = |x| > 0 $. The paper also presents Theorem 2, which generalizes Theorem 1 to fully nonlinear equations of the form $ F[u] = 0 $, where $ F $ satisfies certain conditions. The proof of Theorem 2 relies on the method of moving planes and the maximum principle. The key idea is that the usual maximum principle can be applied to handle the difficulties that might arise in getting the moving plane device started near infinity. The paper also discusses related results, including Theorem A by Gidas, Ni, and Nirenberg, which establishes radial symmetry for solutions of the scalar field equation $ \Delta u - u + u^p = 0 $ in $ \mathbb{R}^n $, and Theorem B by Franchi and Lanconelli, which extends the result to quasilinear equations. Additionally, C. Li extends the result to fully nonlinear equations. The paper also provides an example showing that solutions can decay at infinity slower than logarithmic decay, and another example demonstrating that the symmetric point does not necessarily have to be the origin if the equation depends on $ |x| $. The main contribution of the paper is the proof of Theorem 2, which shows that under certain conditions, all positive solutions of the fully nonlinear equation are radially symmetric about some point in $ \mathbb{R}^n $ and strictly decreasing away from that point.