Nonresonance conditions on the potential with respect to the Fučík spectrum for semilinear Dirichlet problems

Abstract

The existence of solutions for semilinear equations with Dirichlet condition are established under the assumption that the nonlinearity is of linear growth and the asymptotic behavior of its primitive at infinity stays away from the Fučík spectrum.

Multiple Periodic Solutions of Second-Order Ordinary Differential Equations Across Resonance

“…Besides the above cited papers, for related works on resonant problems we also refer the interested reader to see [6,7,12,13,14,16,23,29,30] …”