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
OBERSNEL, Franco;OMARI, PIERPAOLO
2006-01-01
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 $\Omega$.File in questo prodotto:
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