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).

In this paper we qualitatively study radial solutions of the semilinear elliptic equation $\Delta u + u^n = 0$ with $u(0)=1$ and $u'(0)=0$ on positive real line, called Emden-Fowler or Lane-Emden equation. This is great importance in Newtonian astrophysics constant $n$ polytropic index. By introducing a set new variables, can be written as an autonomous system two ordinary differential equation...

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.

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...

Singular initial value problems are investigated. We extend a decomposition method for di¤erent type Emden-Fowler-like equations. Some special cases of the equation are solved as examples, to illustrate the reliableness of the method. The solutions are constructed in the form of a convergent series.

We investigate the dependence on parameters for the discrete boundary value problem connected with the Emden-Fowler equation. A variational method is used in order to obtain a general scheme allowing for investigation the dependence on paramaters of discrete boundary value problems. MSC Subject Classification: 34B16, 39M10

We obtain the optimal system’s generating operators associated to a modification of generalization Emden–Fowler Equation. Using those we characterize all invariant solutions generalized. Moreover, present variational symmetries and corresponding conservation laws, using Noether’s theorem Ibragimov’s method. Finally, classify Lie algebra given equation.

In this paper, we establish two kinds of Emden–Fowler type equations of third order. We investigate the linear and the nonlinear third-order equations, with specified initial conditions, by using the systematic variational iteration method. We corroborate this study by investigating several Emden–Fowler type examples with initial value conditions.