Fu/v cik Spectrum for the Neumann Problem with Indefinite Weights

We obtain a description of the Fu\v{c}ik spectrum associated to the one-dimensional asymmetric problem with indefinite weights $Lu = am(t)u^+ - bn(t)u^-$ in $]T_1, T_2[$, $u'(T_1) = 0 = u'(T_2)$, where $L$ is a Sturm-Liouville operator. Our approach is based on the shooting method.