Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222479 | Nonlinear Analysis: Real World Applications | 2014 | 11 Pages |
Abstract
Many electrorheological fluids are suspensions of solid particles that are exposed to a strong electric field. This causes a dramatic increase of their effective viscosity. In this paper we are concerned with a mathematical problem that is related with this non-Newtonian behavior. More precisely, we study the nonlinear stationary equation âdiv(|âu|p(x)â2âu)+|u|p(x)â2u=f(x,u) in Ω, under Dirichlet boundary conditions, where Ω is a smooth bounded domain in Rn, p>1 is a continuous function, and f(x,u) has a sublinear growth near the origin. Under various natural assumptions, by using the Morse theory in combination with local linking arguments, we obtain the existence of nontrivial weak solutions.
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Authors
VicenÅ£iu D. RÄdulescu, Binlin Zhang,