By the semi-inverse method, a variational principle is obtained for the Lane–Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method. 2002 Elsevier Science Inc. All rights reserved.

We study qualitative properties for nonnegative solutions to a conformally invariant coupled system of fourth order equations involving critical exponents. For defined in the punctured space, there exist essentially two cases analyze. If origin is removable singularity, we use an integral moving spheres method prove that non-singular are rotationally invariant. More precisely, they product sphe...

In this paper‎, ‎numerical solution of‎ ‎general Lane-Emden equation via collocation method based on‎ ‎Double Exponential DE transformation is considered‎. ‎The‎ ‎method converts equation to the nonlinear Volterra integral‎ ‎equation‎. ‎Numerical examples show the accuracy of the method.‎ ‎Also‎, ‎some remarks with respect to run-time‎, computational cost‎ ‎and implementation are discussed.

The D-dimensional cosmological model on the manifold M = R × M1 × M2 describing the evolution of 2 Einsteinian factor spaces, M1 and M2, in the presence of multicomponent perfect fluid source is considered. The barotropic equation of state for mass-energy densities and the pressures of the components is assumed in each space. When the number of the non Ricci-flat factor spaces and the number of...