Eigenvalue problems with indefinite weight

Szulkin, A;Willem, Michel
(1999) Studia Mathematica —

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  • Szulkin, A
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  • Willem, MichelUCLouvain
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Abstract
We consider the linear eigenvalue problem -Delta u = lambda V(x)u, u is an element of D-0(1,2)(Omega), and its nonlinear generalization -Delta(p)u = lambda V(x)u(p-2)u, u is an element of D-0(1,p)(Omega). The set Omega need not be bounded, in particular, Omega = R-N is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence df eigenvalues lambda(n) --> infinity.
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Szulkin, A., & Willem, M. (1999). Eigenvalue problems with indefinite weight. Studia Mathematica. https://hdl.handle.net/2078.5/140463