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 -∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\infty $$\end{document} (resonant or not) and has a superlinear growth at +∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+\infty $$\end{document}, 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.