We consider weak positive solutions of the equation −∆mu = f(u) in the halfplane with zero Dirichlet boundary conditions. Assuming that the nonlinearity f is locally Lipschitz continuous and f(s) > 0 for s > 0, we prove that any solution is monotone. Some Liouville type theorems follow in the case of Lane-Emden-Fowler type equations. Assuming also that |∇u| is globally bounded, our result impli...

In this paper, we use a numerical method involving collocation method with third B-splines as basis functions for solving a class of singular initial value problems (IVPs) of Lane--Emden type equation. The original differential equation is modified at the point of singularity. The modified problem is then treated by using B-spline approximation. In the case of non-linear problems, we first line...

In this paper, Singular initial value problems are investigated by using Taylor series method. The solutions are constructed in the form of a convergent series. The method is applied to Emden-Fowler and Lane-Emden equations.