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An extension of Leray-Schauder degree and applications to nonlinear wave equations. (English) Zbl 0724.47024
The authors construct a topological degree for some classes of monotone mappings which contains F. E. Browder’s degree [Degree theory for nonlinear mappings, Proc. Symp. Pure Math. 45, Pt. 1, Am. Math. Soc., 203-226 (1986; Zbl 0601.47050)] as a special case. The construction builds on both properties of monotone operators and the classical Leray- Schauder degree, and allows very successful applications to the periodic Dirichlet problem for the semilinear wave equation $u_{tt}(t,x)- u_{xx}(t,x)+g(t,x,u(t,x))=h(t,x).$

##### MSC:
 47H05 Monotone operators and generalizations 47J05 Equations involving nonlinear operators (general) 35L05 Wave equation 35L70 Second-order nonlinear hyperbolic equations 55M25 Degree, winding number
Zbl 0601.47050