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...

We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions ar...

A new implicit method has been presented for solving singular initial value problems. The formula has derived in such a way that it excludes the singular point. The method is illustrated by suitable examples (first and second order). To check the results the approximate solutions have been compared to exact solutions KeywordsSingular initial value problems; Lane-Emden equations; Emden-Fowler eq...

In this work, we investigate astrophysical systems in a Newtonian regime using anisotropic matter. For purpose, considered that both radial and tangential pressures satisfy generalized Chaplygin-type equation of state. Using model, found the Lane–Emden for system solved it numerically several sets parameters. Finally, explored mass supported by physical compared with Chandrasekhar mass.