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...

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...

We present a detailed analysis of general relativistic static spherical symmetric distribution in which both the radial and tangential pressures follow master polytropic equation state that generalizes standard treatment avoids appearance singularities system. In particular, we find corresponding Lane-Emden integrate it for wide range values parameters involved. explore parameter space with aim...

Monte Carlo (MC) method played an essential role in many areas of human activity and has found application branches physical science. This paper proposes a computational technique based on MC algorithms to solve Lane–Emden (LE) type equations. We analyze four LE equations arising astrophysics: the positive negative indices polytropic gas spheres, isothermal sphere, white dwarf equation. calcula...

The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in a mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is achieved by truncating to N terms an expansion of the Newtonian potential in spherical Bessel functions. The order N is related to the softening at short dista...

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...

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations rxΔ Δ t p t x τ t 0 on a time scale T; here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on T. Our results in this paper not only extend the results given in Agarwal et al. 2005 , Akin-...