On Bounded Solutions of the Emden–Fowler Equation in a Semi-cylinder

Author: Kozlov V.

Source: Journal of Differential Equations, Volume 179, Number 2, March 2002 , pp. 456-478(23)

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Abstract:

Bounded solutions of the Emden–Fowler equation in a semi-cylinder are considered. For small solutions the asymptotic representations at infinity are derived. It is shown that there are large solutions whose behavior at infinity is different. These solutions are constructed when some inequalities between the dimension of the cylinder and the homogeneity of the nonlinear term are fulfilled. If these inequalities are not satisfied then it is proved, for the Dirichlet problem, that all bounded solutions tend to zero and have the same asymptotics as small solutions.© 2002 Elsevier Science (USA).

Language: English

Document Type: Research article

Affiliations: Department of Mathematics, University of Linköping, Linköping, S-581 83, Sweden

Publication date: 2002-03-01