Continuous spectrum for a class of nonhomogeneous differential operators

Details Continuous spectrum for a class of nonhomogeneous differential operators Continuous spectrum for a class of nonhomogeneous differential operators

2007-06-27

arxiv.org/abs/0706.4045v1

Mathematics

Analysis of PDEs

Scientific paper

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

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