Generalizing the Poincaré–Miranda theorem: the avoiding cones condition
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Abstract
After proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré–Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from \(\pm \)1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.
Keywords
Poincaré–Miranda Fixed point Topological degreeMathematics Subject Classification
47H10 54H25 37C25Notes
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