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2009 Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights
Wei Li, Ping Yan
Abstr. Appl. Anal. 2009: 1-27 (2009). DOI: 10.1155/2009/109757


Consider the half-eigenvalue problem (ϕp(x))+λa(t)ϕp(x+)λb(t)ϕp(x)=0 a.e. t[0,1], where 1<p<, ϕp(x)=|x|p2x, x±()=max{±x(), 0} for x𝒞0:=C([0,1],), and a(t) and b(t) are indefinite integrable weights in the Lebesgue space γ:=Lγ([0,1],),1γ. We characterize the spectra structure under periodic, antiperiodic, Dirichlet, and Neumann boundary conditions, respectively. Furthermore, all these half-eigenvalues are continuous in (a,b)(γ,wγ)2, where wγ denotes the weak topology in γ space. The Dirichlet and the Neumann half-eigenvalues are continuously Fréchet differentiable in (a,b)(γ,γ)2, where γ is the Lγ norm of γ.


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Wei Li. Ping Yan. "Various Half-Eigenvalues of Scalar p-Laplacian with Indefinite Integrable Weights." Abstr. Appl. Anal. 2009 1 - 27, 2009.


Published: 2009
First available in Project Euclid: 16 March 2010

zbMATH: 1188.34018
MathSciNet: MR2539910
Digital Object Identifier: 10.1155/2009/109757

Rights: Copyright © 2009 Hindawi

Vol.2009 • 2009
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