In this paper, we first establish decay estimates for the fractional and higher-order H\'enon-Lane-Emden systems by using a nonlocal average integral estimates, which deduce result of non-existence. Next, apply method scaling spheres introduced in \cite{DQ2} to derive Liouville type theorem. We also construct an interesting example on super $\frac{\alpha}{2}$-harmonic functions (Proposition 1.2).

In this work we study class I interior solutions supported by anisotropic polytropes. The generalized Lane--Emden equation compatible with the embedding condition is obtained and solved for a different set of parameters in both isothermal non--isothermal regimes. For completeness, Tolman mass computed analysed to some extend. As complementary consider impact Karmarkar on functions respectively....

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.

An all new technique has been devised to solve non-linear LaneEmden type equations. This novel technique is based on the Perturbation Iteration Algorithm. In this paper, a few examples are presented for the illustration of the power and wide usability of the proposed method. Moreover, a compare and contrast with the actual solution is provided. It has been evaluated that by employment of this m...