Estimation of the bifurcation parameter in spectral problems for equations with discontinuous operators

We consider the existence of solutions of the eigenvalue problem for nonlinear equations with discontinuous operators in the reflexive Banach space. Coercivity of the corresponding mapping is not supposed. An upper bound for the value of the bifurcation parameter is obtained by the variational method. This result confirms that the upper bound for the value of the bifurcation parameter obtained earlier in spectral problems for elliptic equations with discontinuous nonlinearities is true.