We consider a quasilinear dynamic equation reducing to a half-linear equation, an Emden–Fowler equation or a Sturm–Liouville equation under some conditions. Any nontrivial solution of the quasilinear dynamic equation is eventually monotone. In other words, it can be either positive decreasing (negative increasing) or positive increasing (negative decreasing). In particular, we investigate the a...

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some ...

We classify solutions of finite Morse index of the fractional LaneEmden equation (−∆)su = |u|p−1u in R.

We are concerned with proving that solutions of certain dynamical systems on time scales satisfy some monotoneity conditions. These results then give important results for nth order linear scalar equations. We then give a related result for a third order nonlinear (Emden–Fowler type) dynamic equation.

Introduction The investigation of Lane Emden HLEEL equation has a long standing history Hsee, e.g., @1 10D, to mention only part of a vast literatureL. Recently Schaudt @6D has shown that Picard type iteration scheme may be used to show the existence, uniqueness and regularity of global solutions of LEE , in particular, for n 3 1. In this paper it was shown that straightforward usage of Picard ...

By means of Contractor Iteration Method, we solve and visualize the Lane-Emden(-Fowler) equation Δu+ u = 0, in Ω, u = 0, on ∂Ω. It is shown that the present method converges quadratically as Newton’s method and the computation of Contractor Iteration Method is cheaper than the Newton’s method. Keywords—Positive Solutions; Newton’s Method; Contractor Iteration Method; Eigenpairs.

We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...