The theory of dynamical systems and their widespread applications involve, for example, the Lane–Emden-type equations which are known to arise in initial- boundary-value problems with singularity at time t=0. main objective this paper is make use some mathematical analytic tools techniques order numerically solve reaction–diffusion equations, spherical catalysts biocatalysts, by applying Chebys...

In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane-Emden-Fowler equations with singu...

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.

This research article introduces an efficient method for integrating Lane–Emden–Fowler equations of second-order singular initial value problems (SIVPs) using a pair hybrid block methods with variable step-size mode. The pairs optimized Nyström technique set formulas applied at the step to circumvent singularity beginning interval. formulation is implemented embedded-type approach, resulting in...