Abstract
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.
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Acknowledgements
The authors would like to express their sincere gratitude to the referee for carefully reading the manuscript and valuable comments and suggestions. The first author was partially supported by CNPq Grants 429955/2018-9.
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The first author was partially supported by CNPq/Universal 2018 with Grant 429955/2018-9.
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Silva, E.D., Ribeiro, B. Resonant-Superlinear Elliptic Problems at High-Order Eigenvalues. Mediterr. J. Math. 18, 121 (2021). https://doi.org/10.1007/s00009-021-01762-0
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DOI: https://doi.org/10.1007/s00009-021-01762-0