In this article we consider the existence and uniqueness of local weak solutions to the Emden-Fowler type wave equation tutt − uxx = |u|p−1u in [1, T ]× (a, b) with initial-boundary value conditions in a finite time interval.

We derive a monotonicity formula for solutions of the fractional Hénon-Lane-Emden equation (−∆)u = |x|a|u|p−1u R where 0 < s < 2, a > 0 and p > 1. Then we apply this formula to classify stable solutions of the above equation.

Equation (2) has some oscillation behavior [1-3], In 2012, Liu [4] obtained some oscillation criteria of eq. (1). In the last decades, the Emden-Fowler equations have attracted extensive attention for the relevance to nuclear physics and gaseous dynamics in astrophysics, the oscillation behavior of the Emden-Fowler equations are studied by many scholars [5-10]. In this paper, we further study f...

In this communication, we describe the Homotopy Perturbation Method with Laplace Transform (LT-HPM), which is used to solve the Lane-Emden type differential equations. It's very difficult to solve numerically the Lane-Emden types of the differential equation. Here we implemented this method for two linear homogeneous, two linear nonhomogeneous, and four nonlinear homogeneous Lane-Emden type dif...

We consider the second order differential equation ( a(t)|x′|α sgn x′ )′ + b(t)|x| sgn x = 0 in the super-linear case α < β. We prove the existence of the so-called intermediate solutions and we discuss their coexistence with other types of nonoscillatory and oscillatory solutions. Our results are new even for the Emden–Fowler equation (α = 1).

We introduce an iterative method for computing the first eigenpair (λp, ep) for the pLaplacian operator with homogeneous Dirichlet data as the limit of (μq,uq) as q → p −, where uq is the positive solution of the sublinear Lane-Emden equation −∆puq = μqu q−1 q with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained th...

In this paper we propose, a collocation method for solving nonlinear singular Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infnite interval. This approach is based on a generalized Laguerre polynomial collocation method. This method reduces the solution of this problem to the solution of a system of algebraic equations.We also present the comparison of this wo...