Landesman-Lazer Type like Results for the p-Laplacian

Pavel Drábek ()
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Pavel Drábek: University of West Bohemia, Centre of Applied Mathematics

A chapter in Function Spaces, Differential Operators and Nonlinear Analysis, 2003, pp 289-295 from Springer

Abstract: Abstract We study the Dirichlet boundary value problem for the p-Laplacian of the form $$ - \Delta _p u - \lambda \left| u \right|^{p - 2} u + g(x,u) = f\;in\;\Omega ,\;u = 0\;on\;\partial \Omega , $$ in Ωu = 0 on ∂Ω where $$ \Omega \subset \mathbb{R}^N $$ is a bounded domain with smooth boundary ∂ΩN≥ 1 p> 1, $$f \in C(\bar \Omega ),\lambda > 0$$ λ> 0 is a spectral parameter and gis a bounded function. We give the characterization of the right-hand sides ffor which the Dirichlet problem above is solvable and has multiple solutions.

Keywords: Dirichlet Problem; Dirichlet Boundary; Spectral Parameter; Smooth Boundary; Nonlinear Anal (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-8035-0_18

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DOI: 10.1007/978-3-0348-8035-0_18

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