Multiple variational solutions to nonlinear Steklov problems
type: Item
instance of: scholarly article
title: Multiple variational solutions to nonlinear Steklov problems
zbMATH Open document ID: 1255.35091
author: Carlo D. Pagani
author: Dario Pierotti
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2012-12-06T00:00:00Z
review text: The authors consider the problem of finding a harmonic function \(u\) in a bounded domain \({\Omega \subset {\mathbb R}^N}\), \(N \geq 2,\) satisfying a nonlinear boundary condition of the form \[ \partial_{\nu}u(x)=\lambda\,(\eta(x)u(x)+\mu(x)h(u(x)),\,\, x\in \partial \Omega, \] where \(\mu\) and \(\eta\) are bounded functions and \(h\) is a \({\mathcal{C}^1}\) odd function with subcritical growth at infinity and such that \(\lim_{s\rightarrow \infty} h^{\prime}(s) = +\infty\). By using variants of the mountain pass lemma based on index theory, the authors discuss existence and multiplicity of non trivial solutions to the problem for every value of \(\lambda \).
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35J20
Mathematics Subject Classification ID: 35A15
zbMATH DE Number: 6113127
zbMATH Keywords: harmonic solution
zbMATH Keywords: variational methods
zbMATH Keywords: Steklov eigenvalue problem
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s00030-011-0136-z
OpenAlex ID: W2046571787
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DOI: 10.1007/S00030-011-0136-Z
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description: scientific article; zbMATH DE number 6113127