Upper and Lower Solutions for a Generalized Emden-Fowler Equation

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.

Multiple solutions for boundary value problems of a discrete generalized Emden-Fowler equation

By using critical point theory, some new sufficient conditions for the existence of at least 2N distinct solutions to boundary value problems of a discrete generalized Emden–Fowler equation are obtained. © 2009 Elsevier Ltd. All rights reserved.

Bubbling Solutions for an Anisotropic Emden-Fowler Equation

We consider the following anisotropic Emden-Fowler equation ∇(a(x)∇u) + εa(x)e = 0 in Ω, u = 0 on ∂Ω where Ω ⊂ R is a bounded smooth domain and a(x) is a positive smooth function. We investigate the effect of anisotropic coefficient a(x) on the existence of bubbling solutions. We show that at given local maximum points of a(x), there exists arbitrarily many bubbles. As a consequence, the quanti...

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

On Nodal Solutions to Generalized Emden-fowler Equations

We introduce a new variational method in order to derive results concerning existence and nodal properties of solutions to superlinear equations, and we focus on applications to the equation where h is a Caratheodory function which is odd in u. In the particular case where h is radially symmetric, we prove, for given n 2 N, the existence of a solution having precisely n nodal domains, whereas s...