Continuous spectrum for a class of nonhomogeneous differential operators

Mihai Mihailescu (1) , Vicentiu Radulescu (2)

1 UCV - Department of Mathematics
2 IMAR - "Simion Stoilow" Institute of Mathematics

We study the boundary value problem $-{\rm div}((|\nabla u|^{p_1(x)-2}+|\nabla u|^{p_2(x)-2})\nabla u)=\lambda|u|^{q(x)-2}u$ in $\Omega$, $u=0$ on $\partial\Omega$, where $\Omega$ is a bounded domain in $\RR^N$ with smooth boundary, $\lambda$ is a positive real number, and the continuous functions $p_1$, $p_2$, and $q$ satisfy $1

Mots clés: $p(x)$-Laplace operator; eigenvalue problem; generalized Lebesgue-Sobolev space; critical point; electrorheological fluids

Domaines: Equations aux dérivées partielles [math.AP]

Mihai Mihailescu, Vicentiu Radulescu. Continuous spectrum for a class of nonhomogeneous differential operators. 2007. ⟨hal-00158060⟩