Abstract
We consider the problem of finding a harmonic function u in a bounded domain \({\Omega\subset\mathbb{R}^N}\), N ≥ 2, satisfying a nonlinear boundary condition of the form \({\partial_{\nu}u(x)=\lambda\,\mu(x)h(u(x)), x\in \partial\Omega}\) where μ changes sign and h is an increasing function with superlinear, subcritical growth at infinity. We study the solvability of the problem depending on the parameter λ by using min-max methods.
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Communicated by M. Struwe.
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Pagani, C.D., Pierotti, D. Variational methods for nonlinear Steklov eigenvalue problems with an indefinite weight function. Calc. Var. 39, 35–58 (2010). https://doi.org/10.1007/s00526-009-0300-z
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DOI: https://doi.org/10.1007/s00526-009-0300-z