We prove the existence of two unbounded sequences of strictly positive solutions, obtained respectively as minimum and saddle points of the associated action functional, of the elliptic problem $$\left\{ \begin{array}{cl} -\Delta u = f(x,u) & \mbox{ in }\, \Omega, \\ u = 0 & \mbox{ on }\, \partial \Omega, \end{array} \right.$$ assuming that an oscillatory behaviour at $+\infty$ of $s^{-2} \int_0^s f(x, \xi) d \xi$ occurs locally in $\Omega$.

### Positive solutions of elliptic problems with locally oscillating nonlinearities

#### Abstract

We prove the existence of two unbounded sequences of strictly positive solutions, obtained respectively as minimum and saddle points of the associated action functional, of the elliptic problem $$\left\{ \begin{array}{cl} -\Delta u = f(x,u) & \mbox{ in }\, \Omega, \\ u = 0 & \mbox{ on }\, \partial \Omega, \end{array} \right.$$ assuming that an oscillatory behaviour at $+\infty$ of $s^{-2} \int_0^s f(x, \xi) d \xi$ occurs locally in $\Omega$.
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2006
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/1697222
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