Emden–Fowler type equations are nonlinear differential that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific equation emerges queuing theory context approximation voltages under well-known power flow model. Thus, place the electrical engineering. We derive properties continuous solution study behavior ...

Abstract We prove that the Dirichlet problem for Lane–Emden equation in a half-space has no positive solution is monotone normal direction. As consequence, this does not admit any classical bounded on finite strips. This question long history and our result solves long-standing open problem. Such nonexistence was previously available only solutions or under restriction power nonlinearity. The e...

In this paper we study the existence of uniform a priori estimates for positive solutions to Navier problems higher order Lane–Emden equations \begin{equation}\label{0-0} (-\Delta)^{m}u(x)=u^{p}(x), \quad x\in\Omega, \end{equation} all large exponents $p$, where $\Omega\subset\mathbb{R}^{n}$ is star-shaped or strictly convex bounded domain with $C^{2m-2}$ boundary, $n\geq4$, and $2\leq m\leq\fr...

In this paper we propose a class of second derivative multistep methods for solving some well-known classes of LaneEmden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-...

This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with previous work [R. Guo, Phys. Plasmas \textbf{27}, 122104 (2020)]. We find that equation of state can lead to without any other assumptions one dimension. In higher dimensions, extra assumption global must only depend on energy is still needed. addition, self-con...