We prove an Ambrosetti-Prodi type result for a Neumann problem associated to the equation u + f(x, u(x)) = µ when the nonlinearity has the following form: f(x, u):= a(x)g(u) − p(x). The assumptions considered generalize the classical one, f(x, u) → +∞ as |u| → +∞, without requiring any uniformity condition in x. The multiplicity result which characterizes these kind of problems will be proved by means of the shooting method.
Ambrosetti-prodi type result to a neumann problem via a topological approach / Sovrano, E.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 11:2(2018), pp. 345-355. [10.3934/dcdss.2018019]
Ambrosetti-prodi type result to a neumann problem via a topological approach
Sovrano E.
2018
Abstract
We prove an Ambrosetti-Prodi type result for a Neumann problem associated to the equation u + f(x, u(x)) = µ when the nonlinearity has the following form: f(x, u):= a(x)g(u) − p(x). The assumptions considered generalize the classical one, f(x, u) → +∞ as |u| → +∞, without requiring any uniformity condition in x. The multiplicity result which characterizes these kind of problems will be proved by means of the shooting method.
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