Topological degree for elliptic operators in unbounded cylinders
type: Item
instance of: scholarly article
title: Topological degree for elliptic operators in unbounded cylinders
zbMATH Open document ID: 0952.35038
author: A. I. Volpert
author: Vitaly Volpert
author: Jean-François Collet
published in: Advances in Differential Equations
publication date: 2000-08-21T00:00:00Z
review text: The authors construct a topological degree for elliptic operators \[ A(u) = a(x)\Delta u + \sum_{i=1}^m b_i(x)\frac{\partial u}{\partial x_i} + F(x,u) +K(u),\quad \Lambda u = \left.\left(\alpha\frac{\partial u}{\partial\nu} + \beta(x)u\right) \right|_{\partial\Omega}, \] in an unbounded cylinder \(\Omega\). Here \(u=\{u_1,\ldots,u_p\}\), \(F\) is a vector-valued function and \(K\) is a finite-dimensional operator included in view of applications: the traveling waves investigation. Standard degree theory is constructed in weighted Hölder spaces.
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 1493613
zbMATH Keywords: topological degree
zbMATH Keywords: semilinear elliptic operators in unbounded cylinders
zbMATH Keywords: semilinear evolution equations
zbMATH Keywords: traveling waves
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1493613