Nsoki Mavinga, Mubenga N. Nkashama
Abstract:
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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