Electron. J. Diff. Equ., Vol. 2016 (2016), No. 210, pp. 1-7.

Nonlinear Fredholm alternative for the p-Laplacian under nonhomogeneous Neumann boundary condition

Gustavo Ferron Madeira

The nonlinear Fredholm alternative for the p-Laplacian in higher dimensions is established when nonhomogeneous terms appear in the equation and in the Neumann boundary condition. Further, the geometry of the associated energy functional is described and compared with the Dirichlet counterpart. The proofs require only variational methods.

Submitted August 12, 2015. Published August 2, 2016.
Math Subject Classifications: 35J60, 35J65, 47J30, 49N10.
Key Words: Quasilinear elliptic equations; nonlinear Fredholm alternative; p-Laplacian; Neumann boundary value problem; variational methods; global minimizer.

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Gustavo Ferron Madeira
Departamento de Matemática
Universidade Federal de São Carlos
13.565-905, São Carlos (SP), Brazil
email: gfmadeira@dm.ufscar.br

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