A continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces

dc.creatorMihailescu, Mihai
dc.creatorRadulescu, Vicentiu
dc.date2007-11-06
dc.date.accessioned2026-07-07T08:41:02Z
dc.date.available2026-07-07T08:41:02Z
dc.descriptionWe study the nonlinear eigenvalue problem $-{\rm div}(a(|\nabla u|)\nabla u)=λ|u|^{q(x)-2}u$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a bounded open set in $\RR^N$ with smooth boundary, $q$ is a continuous function, and $a$ is a nonhomogeneous potential. We establish sufficient conditions on $a$ and $q$ such that the above nonhomogeneous quasilinear problem has continuous families of eigenvalues. The proofs rely on elementary variational arguments. The abstract results of this paper are illustrated by the cases $a(t)=t^{p-2}\log (1+t^r)$ and $a(t)= t^{p-2} [\log (1+t)]^{-1}$.
dc.identifierhttps://arxiv.org/abs/0711.0904
dc.identifierhttp://arxiv.org/abs/0711.0904
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/141555
dc.subjectAnalysis of PDEs
dc.subject35D05, 35J60, 35J70, 58E05, 68T40, 76A02
dc.titleA continuous spectrum for nonhomogeneous differential operators in Orlicz-Sobolev spaces
dc.typetext

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