Advances in Differential Equations

Topological degree for elliptic operators in unbounded cylinders

J. F. Collet, V. A. Volpert, and A. I. Volpert

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Semilinear elliptic operators in unbounded cylinders are considered. It is shown that under some conditions the operators are Fredholm and proper. A topological degree for these operators is defined and shown to be unique. The results are applied to operators describing traveling waves.

Article information

Adv. Differential Equations, Volume 4, Number 6 (1999), 777-812.

First available in Project Euclid: 15 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations
Secondary: 47H11: Degree theory [See also 55M25, 58C30] 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 58C30: Fixed point theorems on manifolds [See also 47H10]


Volpert, V. A.; Volpert, A. I.; Collet, J. F. Topological degree for elliptic operators in unbounded cylinders. Adv. Differential Equations 4 (1999), no. 6, 777--812.

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