We obtain the optimal system’s generating operators associated to a modification of generalization Emden–Fowler Equation. Using those we characterize all invariant solutions generalized. Moreover, present variational symmetries and corresponding conservation laws, using Noether’s theorem Ibragimov’s method. Finally, classify Lie algebra given equation.

We classify solutions of finite Morse index of the fractional LaneEmden equation (−∆)su = |u|p−1u in R.

In this work we consider the existence of positive singular solutions style='text-indent:20px;'> \begin{document}$ \begin{equation} \left\{ \begin{array}{lcl} \hfill -\Delta u_1 & = \lambda_1 | \nabla u_2|^p \qquad \mbox{ in } \Omega, \\ u_2 \lambda_2 u_1|^q 0 on \partial \end{array}\right.\;\;\;\;\;\;\;(1) \end{equation} $\...