Continuous spectrum for a class of nonhomogeneous differential operators

dc.creatorMihailescu, Mihai
dc.creatorRadulescu, Vicentiu
dc.date2007-06-27
dc.date.accessioned2026-07-07T08:12:42Z
dc.date.available2026-07-07T08:12:42Z
dc.descriptionWe study the boundary value problem $-{\rm div}((|\nabla u|^{p_1(x)-2}+|\nabla u|^{p_2(x)-2})\nabla u)=λ|u|^{q(x)-2}u$ in $Ω$, $u=0$ on $\partialΩ$, where $Ω$ is a bounded domain in $\RR^N$ with smooth boundary, $λ$ is a positive real number, and the continuous functions $p_1$, $p_2$, and $q$ satisfy $1<p_2(x)<q(x)<p_1(x)<N$ and $\max_{y\in\barΩ}q(y)<\frac{N p_2(x)}{N-p_2(x)}$ for any $x\in\barΩ$. The main result of this paper establishes the existence of two positive constants $λ_0$ and $λ_1$ with $λ_0\leqλ_1$ such that any $λ\in[λ_1,\infty)$ is an eigenvalue, while any $λ\in(0,λ_0)$ is not an eigenvalue of the above problem.
dc.identifierhttps://arxiv.org/abs/0706.4045
dc.identifierhttp://arxiv.org/abs/0706.4045
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132543
dc.subjectAnalysis of PDEs
dc.subject35D05, 35J60, 35J70, 58E05, 68T40, 76A02
dc.titleContinuous spectrum for a class of nonhomogeneous differential operators
dc.typetext

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