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Computation of topological degree for nonlinear operators and applications. (English) Zbl 1169.47043
This paper focuses on ordered Banach spaces that are also lattices and provides some formulas for the computation of the topological degree of a class of operators (called quasi-additive) that are not necessarily cone mappings. An application to a Sturm--Liouville problem is also provided.

##### MSC:
 47H11 Degree theory (nonlinear operators) 47N20 Applications of operator theory to differential and integral equations
##### Keywords:
cone; lattice; topological degree; Sturm-Liouville problems
Full Text:
##### References:
 [1] Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM rev. 18, 620-709 (1976) · Zbl 0345.47044 · doi:10.1137/1018114 [2] Amann, H.: On the number of solutions of nonlinear equations in ordered Banach spaces, J. funct. Anal. 11, 346-384 (1972) · Zbl 0244.47046 · doi:10.1016/0022-1236(72)90074-2 [3] Deimling, K.: Nonlinear functional analysis, (1985) · Zbl 0559.47040 [4] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones, (1988) · Zbl 0661.47045 [5] Lucxemburg, W. A. J.; Zaanen, A. C.: Riesz space, vol. 1, (1971) [6] Sun, Jingxian; Liu, Xiaoying: Computation for topological degree and its applications, J. math. Anal. appl. 202, 785-796 (1996) · Zbl 0866.47043 · doi:10.1006/jmaa.1996.0347