@article {Fonda2016, title = {Generalizing the Poincar{\'e}{\textendash}Miranda theorem: the avoiding cones condition}, journal = {Annali di Matematica Pura ed Applicata (1923 -)}, volume = {195}, number = {4}, year = {2016}, month = {Aug}, pages = {1347{\textendash}1371}, abstract = {
After proposing a variant of the Poincar{\'e}{\textendash}Bohl theorem, we extend the Poincar{\'e}{\textendash}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 \$\$\backslashpm \$\${\textpm}1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points.
}, issn = {1618-1891}, doi = {10.1007/s10231-015-0519-6}, url = {https://doi.org/10.1007/s10231-015-0519-6}, author = {Alessandro Fonda and Paolo Gidoni} }