Structure of the Fučík spectrum and existence of solutions for equations with asymmetric nonlinearities (Q2719731)

The authors gave a description of the Fučík spectrum for a selfadjoint operator \(L :\text{dom}\,L\subset L^2(\Omega)\rightarrow L^2(\Omega)\) away from its essential spectrum. Here \(\Omega\subset\mathbb R^N\) is a bounded domain. In some cases the Fučík spectrum can be completely described. These results are applied, for example, to the equation with jumping nonlinearity \(Lu = \alpha u^+ - \beta u^- +g(x,u)\), a function \(g\) has a sublinear growth in \(u\) at infinity. NEWLINENEWLINEPrevious results: \textit{Th. Gallouët} and \textit{O. Kavian} [Commun. Partial Differ. Equations 7, 325--342 (1982; Zbl 0497.35080)]; \textit{Nguyên Phuong Các} [J. Differ. Equations 80, No. 2, 379--404 (1989; Zbl 0713.35036)]; \textit{C. A. Magalhães} [Commun. Partial Differ. Equations 15, No. 9, 1265-1292 (1990; Zbl 0726.35044)]; \textit{M. Schechter} [NoDEA, Nonlinear Differ. Equ. Appl. 4, No. 4, 459--476 (1997; Zbl 0893.35039)].