The present paper is concerned with the asymptotic behavior of solutions to a class noncanonical third-order Emden–Fowler delay differential equations superlinear neutral term. Using Riccati-type transformation as well integral criteria, we establish some new sufficient conditions guaranteeing that every solution equation considered either oscillates or converges zero asymptotically. results ar...

Abstract In this paper, we study the oscillation of a class third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales. By using Riccati transformation and integral inequality, establish several new theorems to ensure that each solution equation oscillates or asymptotically approaches zero, results in literature are supplemented extended. Examples given illustr...

Using the scalar and tensor virial equations, the Lane-Emden equation expressing the hydrostatic equilibrium and small oscillations around the equilibrium, we show how the cosmological constant Λ affects various astrophysical quantities important for large matter conglomeration in the universe. Among others we examine the effect of Λ on the polytropic equation of state for spherically symmetric...

It is shown how the Python library Sympy can be used to compute symbolically the coefficients of the power series solution of the Lane-Emden equation (LEE). Sympy is an open source Python library for symbolic mathematics. The power series solutions are compared to the numerically computed solutions using matplotlib. The results of a run time measurement of the implemented algorithm are discusse...

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...

Abstract The purpose of this paper is to analyze the conformally flat spherically symmetric fluid distribution with generalized polytropic equations state. We have developed two different framework for definitions polytropes. frameworks development modified Lane–Emden equation are presented both cases. condition used calculate anisotropy factor which transform considered systems into consistent...

where n is a real constant andf(y) is a real-valued function of the variabley, hasmany applications inmathematical physics and astrophysics. Equation (1), for certain fixed values of n and f(y), models several phenomena such as the theory of stellar structure, the thermal behavior of a spherical cloud of gas, isothermal gaseous sphere, and the theory of thermionic currents [1–3]. Several method...

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.