Abstract. In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, ẍ+αxẋ+βx+γx = 0,which preserves the form of the time independent integral, conservative Hamiltonian and the equation of motion. Generalizing this transformation we prove the existence of non...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

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...

In this paper we prove unique continuation principles for some systems of elliptic partial differential equations satisfying a suitable superlinearity condition. As an application, obtain nonexistence nontrivial (not necessarily positive) radial solutions the Lane-Emden system posed in ball, critical and supercritical regimes. Some our results also apply to general fully nonlinear operators, su...

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...