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Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space. (English) Zbl 1212.47051
Summary: In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.
MSC:
47J05 Equations involving nonlinear operators (general)
47H11 Degree theory for nonlinear operators
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47H10 Fixed-point theorems
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