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Existence and uniqueness of solutions of nonlinear Neumann problems. (English) Zbl 0633.35042
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 J. Spruck [Commun. Partial Differ. Equations 8, 1605-1620 (1983; Zbl 0534.35055)].

##### MSC:
 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35B50 Maximum principles in context of PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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##### References:
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