Blow-up Solution for $4$-dimensional Generalized Emden-Fowler Equation with Exponential Nonlinearity

The Generalized Emden-Fowler Equation

We give the description of nonlinear nonautonomous ordinary differential equations of order n with a so-called reducible linear part. The group classification of generalized Emden-Fowler equations of the mentioned class is done. We have found such laws of the variation of f(x) that the equation admits one, two, or tree one-parameter Lie groups.

Blow-up for the 1d Nonlinear Schrödinger Equation with Point Nonlinearity Ii: Supercritical Blow-up Profiles

We consider the 1D nonlinear Schrödinger equation (NLS) with focusing point nonlinearity, (0.1) i∂tψ + ∂ 2 xψ + δ|ψ|p−1ψ = 0, where δ = δ(x) is the delta function supported at the origin. In the L supercritical setting p > 3, we construct self-similar blow-up solutions belonging to the energy space Lx ∩Ḣ x. This is reduced to finding outgoing solutions of a certain stationary profile equation. ...

Asymptotic Behaviour of the Solution for the Singular Lane-emden-fowler Equation with Nonlinear Convection Terms

We show the exact asymptotic behaviour near the boundary for the classical solution to the Dirichler problem −∆u = k(x)g(u) + λ|∇u| , u > 0, x ∈ Ω, u ̨̨

A Diffusion Equation with Exponential Nonlinearity Recant Developments

The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...

Existence of Solutions to Boundary Value Problems for the Discrete Generalized Emden-Fowler Equation