We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schrödinger-Newton model in any space dimension d. Our result is based on a careful analysis of the corresponding system of second order differential equations. It turns out that d = 6 is critical for the existence of finite energy solutions and the equations for positive spherically symmetric s...

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 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...

Polytropic models play a very important role in galactic dynamics and in the theory of stellar structure and evolution. However, in general, the solution of the Lane-Emden equation can not be given analytically but only numerically. In this paper we give a good analytic approximate solution of the Lane-Emden equation. This approximation is very good for any finite polytropic index n and for the...

We introduce an iterative method for computing the first eigenpair (λp, ep) for the pLaplacian operator with homogeneous Dirichlet data as the limit of (μq,uq) as q → p −, where uq is the positive solution of the sublinear Lane-Emden equation −∆puq = μqu q−1 q with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained th...