Traditional Adomian decomposition method (ADM) usually fails to solve singular initial value problems of Emden-Fowler type. To overcome this shortcoming, a new and effective modification of ADM that only requires calculation of the first Adomian polynomial is formally proposed in the present paper. Three singular initial value problems of Emden-Fowler type with , 1 α  , 2 and , 2  and have be...

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.

We consider a quasilinear dynamic equation reducing to a half-linear equation, an Emden–Fowler equation or a Sturm–Liouville equation under some conditions. Any nontrivial solution of the quasilinear dynamic equation is eventually monotone. In other words, it can be either positive decreasing (negative increasing) or positive increasing (negative decreasing). In particular, we investigate the a...

In this article, we apply blow-up analysis to study pointwise a priori estimates for some p-Laplacian equations based on Liouville type theorems. With newly developed techniques, first extend the classical results of interior gradient harmonic function that p-harmonic function, i.e., solution Δpu = 0, x ∈ Ω. We then obtain singularity and decay sign-changing Lane-Emden-Fowler equation −Δpu |u|λ...

Consider the Emden-Fowler sublinear dynamic equation (0.1) x(t) + p(t)x(σ(t)) = 0, where p ∈ C(T, R), where T is a time scale, 0 < α < 1, α is the quotient of odd positive integers. When p(t) is allowed to take on negative values, we obtain a Belohorec-type oscillation theorem for (0.1). As an application, we get that the sublinear difference equation (0.2) ∆x(n) + p(n)x(n+ 1) = 0, is oscillato...

When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation. The result obtained can be applied to equations with coefficients of the nonlinear term growing exponentially. The proof is based on the super an...