Topological degree for a class of elliptic operators in \(\mathbb{R}^n\). (English) Zbl 0956.35038

Barillon, Christelle; Volpert, Vitaly A.

Topol. Methods Nonlinear Anal. 14, No. 2, 275-293 (1999).

The authors construct a topological degree for elliptic operators \[ A(u) = a(x)\Delta u + \sum_{i=1}^n b_i(x)\frac{\partial u}{\partial x_i} + F(x,u), \] where \(x\in\mathbb R^n\), \(u=(u_1,\ldots,u_p)\), \(F(x,u)=(F_1(x,u),\ldots,F_p(x,u))\). In contrast to the previous article V. A. Volpert, A. I. Volpert and J. F. Collet [Adv. Differ. Equ. 4, No. 6, 777-812 (1999; Zbl 0952.35038)] the degree is defined in the whole \(\mathbb R^n\). Further, the theory is applied to a reaction-diffusion problem.

Reviewer: Serghey G.Suvorov (Donetsk)

MSC:

35J60	Nonlinear elliptic equations
47H11	Degree theory for nonlinear operators
47N20	Applications of operator theory to differential and integral equations

Keywords:

elliptic operators; unbounded domains; reaction-diffusion system; topological degree

Citations:

Zbl 0952.35038