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...

We compute multiprecision solutions of the Lane–Emden equation. This differential equation arises when introducing the well-known polytropic model into the equation of hydrostatic equilibrium for a nondistorted star. Since such multiprecision computations are time-consuming, we apply to this problem parallel programming techniques and thus the execution time of the computations is drastically r...

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...

Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent standard software packages are available for ODEs, there are for good reasons no standard numerical continuation toolboxes available for parti...

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

A numerical method based on B-spline is developed to solve the time-dependent Emden-Fowler-type equations. We also present a reliable new algorithm based on B-spline to overcome the difficulty of the singular point at 0 x = . The error analysis of the method is described. Numerical results are given to illustrate the efficiency of the proposed method.

We give the description of nonlinear nonautonomous ordinary differential equations of order n with a so-called reducible linear part. The group classification of generalized Emden-Fowler equations of the mentioned class is done. We have found such laws of the variation of f(x) that the equation admits one, two, or tree one-parameter Lie groups.

In this article, we apply blow-up analysis to study pointwise a priori estimates for some p-Laplacian equations based on Liouville type theorems. With newly developed techniques, first extend the classical results of interior gradient harmonic function that p-harmonic function, i.e., solution Δpu = 0, x ∈ Ω. We then obtain singularity and decay sign-changing Lane-Emden-Fowler equation −Δpu |u|λ...

We discuss the existence of solutions with oblique asymptotes to a class of second order nonlinear ordinary differential equations by means of Lyapunov functions. The approach is new in this field and allows for simpler proofs of general results regarding Emden-Fowler like equations.