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...

In this article Differential Transformation Method (DTMs) is considered to find exact and approximate solutions of singular Initial Value Problems (IVPs) of the Lane-Emden type in second-order Ordinary Differential Equations (ODEs). The method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series so...

We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present proof of local existence positive radial solutions near $0$ under suitable conditions on $K$. Moreover, we provide a priori estimates $\infty $ when $r^{-\ell }K(r)$ for $\ell \ge -p$ is bounded $.

We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations.We study the case of superlinear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate th...

The homotopy analysis method [1, 2], is developed to search the accurate asymptotic solutions of nonlinear problems. This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3, 4], the Korteweg-de Vries-type equations [5, 6], nonlinear heat transfer [7, 8], finance problems [9, 10], Riemann problems related to nonlinear shallow w...