Chunshan Zhao

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In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions −div(|∇u| p(x)−2 ∇u) + |u| p(x)−2 u = f(x, u) in Ω, u = 0 on ∂Ω. We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also(More)
In this paper we study the shape of least-energy solutions to the quasilinear problem ε m ∆mu − u m−1 + f (u) = 0 with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that as ε → 0 + , the global maximum point Pε of least-energy solutions goes to a point on the boundary ∂Ω at the rate of o(ε) and this point on the(More)
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