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Topological degree for elliptic operators in unbounded cylinders. (English) Zbl 0952.35038
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.

##### MSC:
 35J60 Nonlinear elliptic equations 47H11 Degree theory for nonlinear operators 47J35 Nonlinear evolution equations