In this paper we establish an existence theorem of strong solutions to a perturbed Neumann problem of the type \begin{displaymath} \left\{ \begin{array}{ll} -\Delta u = \alpha(x)f(u)+\lambda g(x,u) & \mbox{in\ } \Omega \\ \frac{\partial u}{\partial \nu}=0 & \mbox{on\ } \partial \Omega \end{array}\right. \end{displaymath} In particular, our solutions take their values in a fixed real interval. This latter fact allows us to state a multiplicity result assuming on $f$ an oscillating behavior.
Existence and multiplicity of solutions to a perturbed Neumann problem
ANELLO, Giovanni
2007-01-01
Abstract
In this paper we establish an existence theorem of strong solutions to a perturbed Neumann problem of the type \begin{displaymath} \left\{ \begin{array}{ll} -\Delta u = \alpha(x)f(u)+\lambda g(x,u) & \mbox{in\ } \Omega \\ \frac{\partial u}{\partial \nu}=0 & \mbox{on\ } \partial \Omega \end{array}\right. \end{displaymath} In particular, our solutions take their values in a fixed real interval. This latter fact allows us to state a multiplicity result assuming on $f$ an oscillating behavior.File in questo prodotto:
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