Chunshan Zhao

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We continue our work (Y. Li, C. Zhao in J Differ Equ 212:208-233, 2005) to study the structure of positive solutions to the equation epsilon(m) Delta(m)u - u(m-1) + f(u) = 0 with homogeneous Neumann boundary condition in a smooth bounded domain of RN (N >/= 2). First, we study subcritical case for 2 < m < N and show that after passing by a sequence positive(More)
The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any Lr (r > 3) global bounded non-stationary solution to the MHD equations approaches the(More)
This paper presents a novel minimally-invasive catheter-based acoustic interrogation device for real-time monitoring the dynamics of the lower esophageal sphincter (LES). Dysfunction of the LES could result gastrointestinal (GI) diseases, such as gastroesophageal reflux disease (GERD). A micro-oscillator actively emitting sound wave at 16 kHz is located at(More)
Abstract. In this paper we study the shape of least-energy solutions to the quasilinear problem ε∆mu−u + 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 boundary(More)
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 article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u|p(x)−2∇u) + |u|p(x)−2u = λa(x)|u|γ(x)−2u+ Fu(x, u, v) in R , − div |∇v|q(x)−2∇v) + |v|q(x)−2v = λb(x)|v|δ(x)−2v + Fv(x, u, v) in R , u ∈W 1,p(·)(RN ), v ∈W 1,q(·)(RN ), where the corresponding functional does not(More)
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