Electron. J. Diff. Eqns., Vol. 2009(2009), No. 93, pp. 1-12.

A biharmonic elliptic problem with dependence on the gradient and the Laplacian

Paulo C. Carriao, Luiz F. O. Faria, Olimpio H. Miyagaki

Abstract:
We study the existence of solutions for nonlinear biharmonic equations that depend on the gradient and the Laplacian, under Navier boundary condition. Our main tools are an iterative scheme of the mountain pass "aproximated" solutions, and the truncation method developed by de Figueiredo, Girardi and Matzeu.

Submitted March 22, 2009. Published August 6, 2009.
Math Subject Classifications: 31B30, 35G30, 35J40, 47H15.
Key Words: Biharmonic; Navier boundary condition; truncation techniques; iteration method.

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Paulo C. Carrião
Departamento de Matemática, Universidade Federal de Minas Gerais
31270-010 Belo Horizonte (MG), Brazil
email: carrion@mat.ufmg.br
Luiz F. O. Faria
Departamento de Matemática, Universidade Federal de Juiz de Fora
36036-330 Juiz de Fora (MG), Brazil
Universidade Federal de Minas Gerais
email: luiz.faria@ufjf.edu.br
Olímpio H. Miyagaki
Departamento de Matemática, Universidade Federal de Viçosa
36571-000 Viçosa (MG), Brazil
email: olimpio@ufv.br

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