Journal
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume 462, Issue 2073, Pages 2625-2641Publisher
ROYAL SOCIETY
DOI: 10.1098/rspa.2005.1633
Keywords
p(x)-Laplace operator; generalized Lebesgue-Sobolev space; critical point; weak solution; electrorheological fluids
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We study the boundary value problem -div(a(x, del u)) = lambda(mu(gamma-1)-mu(beta-1)) in ohm u=0 on partial derivative ohm, where ohm is a smooth bounded domain in R-N and div(a(x, del u)) is a p(x)-Laplace type operator, with 1 < beta < gamma < inf(x is an element of ohm)p(x). We prove that if is large enough then there exist at least two non-negative weak solutions. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with adequate variational methods and a variant of the Mountain Pass lemma.
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