Fourth-order elliptic problems involving concave-superlinear nonlinearities
DOI:
https://doi.org/10.12775/TMNA.2022.011Keywords
Fourth-order elliptic problems, variational methods, concave-superlinear elliptic problems, nonquadraticity conditionAbstract
The existence of solutions for a huge class of superlinear elliptic problems involving fourth-order elliptic problems defined on bounded domains under Navier boundary conditions is established. To this end we do not apply the well-known Ambrosetti-Rabinowitz condition. Instead, we assume that the nonlinear term is nonquadratic at infinity. Furthermore, the nonlinear term is a concave-superlinear function which can be indefinite in sign. In order to apply variational methods we employ some delicate arguments recovering some kind of compactness.References
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