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...

We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem −∆u = k(x)g(u) + λ|∇u| , u > 0, x ∈ Ω, u ̨̨

Herein, we adduce, analyze, and come up with spectral collocation procedures to iron out a specific class of nonlinear singular Lane–Emden (LE) equations generalized Caputo derivatives that appear in the study astronomical objects. The offered solution is approximated as truncated series normalized shifted Jacobi polynomials under assumption exact an element L2. method used solver obtain unknow...

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...