We consider a class of singular systems of Lane-Emden type      ∆u + λu p 1 v q 1 = 0, x ∈ D, a smooth domain in R n. In case the system is sublinear we prove existence of a positive solution. If D is a ball in R n , we prove both existence and uniqueness of positive radially symmetric solution.

A new and efficient numerical approach is developed for solving nonlinear Lane-Emden type equations via Bernoulli operational matrix of differentiation.The fundamental structure of the presentedmethod is based on theTaumethod togetherwith theBernoulli polynomial approximations in which a new operational matrix is introduced. After implementation of our scheme, the main problem would be transfor...

For 0 < p − 1 < q and either ǫ = 1 or ǫ = −1, we prove the existence of solutions of −∆pu = ǫu q in a cone CS , with vertex 0 and opening S, vanishing on ∂CS , under the form u(x) = |x|ω( x |x|). The problem reduces to a quasilinear elliptic equation on S and existence is based upon degree theory and homotopy methods. We also obtain a non-existence result in some critical case by an integral ty...