Resonant-Superlinear Elliptic Problems at High-Order Eigenvalues

This work establishes existence of solution for resonant-superlinear elliptic problems using an appropriate Linking Theorem. The nonlinearity behaves as an asymptotic linear function at $$-\infty $$ (resonant or not) and has a superlinear growth at $$+\infty $$ , with the eventual resonance phenomena occurring in a high order eigenvalue for the associated linear problem. Our main theorems are stated without the well-known Ambrosetti–Rabinowitz condition.