Electron. J. Differential Equations, Vol. 2017 (2017), No. 167, pp. 1-16.

Multiplicity of solutions to fourth-order superlinear elliptic problems under Navier conditions

Edcarlos D. da Silva, Thiago Rodrigues Cavalcante

Abstract:
We establish the existence and multiplicity of solutions for a class of fourth-order superlinear elliptic problems under Navier conditions on the boundary. Here we do not use the Ambrosetti-Rabinowitz condition; instead we assume that the nonlinear term is a nonlinear function which is nonquadratic at infinity.

Submitted March 1, 2017. Published July 5, 2017.
Math Subject Classifications: 35J20, 35J25, 35J50.
Key Words: Fourth order elliptic problems; variational methods; multiplicity of solutions; superlinear elliptic problems; nonquadraticity condition.

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Edcarlos Domingos da Silva
Universidade Federal de Goiás
IME, Caixa Postal 131
CEP: 74001-970, Goiânia - GO, Brazil
email: edcarlos@ufg.br
Thiago Rodrigues Cavalcante
Universidade Federal de Goiáas
IME, Caixa Postal 131
CEP: 74001-970, Goiânia - GO, Brazil
email: thiagocavalcantegyn@gmail.com

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