Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 197-205.

Steklov spectrum and nonresonance for elliptic equations with nonlinear boundary conditions

Nsoki Mavinga, Mubenga N. Nkashama

This article is devoted to the solvability of second order elliptic partial differential equations with nonlinear boundary conditions. We prove existence results when the nonlinearity on the boundary interacts, in some sense, with the Steklov spectrum. We obtain nonresonance results below the first Steklov eigenvalue as well as between two consecutive Steklov eigenvalues. Our method of proof is variational and relies mainly on minimax methods in critical point theory.

Published September 25, 2010.
Math Subject Classifications: 35J65, 35J20.
Key Words: Steklov eigenvalues; elliptic equations; nonlinear boundary conditions; minimax methods.

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Nsoki Mavinga
Department of Mathematics, University of Rochester
Rochester, NY 14627-0138, USA
email: mavinga@math.rochester.edu
Mubenga N. Nkashama
Department of Mathematics, University of Alabama at Birmingham
Birmingham, AL 35294-1170, USA
email: nkashama@math.uab.edu

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