Spectra of fourth-order quasilinear problems

Jiří Benedikt

Mathematics and Computers in Simulation (MATCOM), 2007, vol. 76, issue 1, 13-17

Abstract: We are interested in spectra of the Dirichlet, Navier and Neumann boundary value problem for the fourth-order quasilinear equation(|u″|p−2u″)″=λ|u|p−2uin[0,1],where λ∈R and p>1. For p=2 the equation reduces to the linear beam equation, u(4)=λu. The operator on the left-hand side is often called a p-biharmonic operator. We introduce recent results on the properties of the spectra, and also an optimization algorithm which is useful for figuring them.

Keywords: p-Biharmonic operator; Nonlinear spectral theory (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:76:y:2007:i:1:p:13-17

DOI: 10.1016/j.matcom.2007.01.027

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