The paper deals with the problem \[ \text{div}(|\nabla u|^{p- 2}\nabla u)+ f(x, u, \nabla u)= 0 \] in \(\mathbb{R}^N\), where \(1< p< N\), \(N\geq 3\). The author employes the classical Schauder fixed point theorem and the subsolution-supersolution technique for the \(p\)-Laplacian. The existence and asymptotic behaviour of decaying positive solutions are given under different assumptations on the function \(f\). Also, the existence of infinitely many positive solutions bounded above and below are established.