Existence and uniqueness of solutions of nonlinear Neumann problems
Existence of non-trivial solutions is proved by means of upper and lower solutions. The solutions are then classified and uniqueness is obtained in certain classes. The results are optimal in the sense that our conditions are necessary and sufficient. We also deduce existence results for problems in \({\mathbb{R}}^ N\). Related papers are by the authors [Trans. Am. Math. Soc. 303, 487-501 (1987; Zbl 0633.35041)] and by \textit{J. Spruck} [Commun. Partial Differ. Equations 8, 1605-1620 (1983; Zbl 0534.35055)].
scientific article; zbMATH DE number 4030071
scientific article