We address the solvability of critical Lane-Emden system in a smooth bounded domain with small spherical hole radius ϵ>0. prove that admits family positive solutions concentrate around center as ϵ→0, obtaining concrete qualitative description well. To best our knowledge, this is first existence result for on domain, while non-existence star-shaped domains has been known since early 1990s due to...

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-...

We propose a new application of the successive linearization method for solving singular initial and boundary value problems of Lane-Emden type. To demonstrate the reliability of the proposed method, a comparison is made with results from existing methods in the literature and with exact analytical solutions. It was found that the method is easy to implement, yields accurate results, and perfor...

The isothermal gas sphere is a particular type of Lane-Emden equation and used widely to model many problems in astrophysics, like the formation stars, star clusters galaxies. In this paper, we present computational scheme simulate conformable fractional using an artificial neural network (ANN) technique, compare obtained results with analytical solution deduced Taylor series. We performed our ...