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彭双阶, Thomas Bartsch, Shuangjie Peng*
,-0001,():
-1年11月30日
We study the radially symmetric Schrödinger equation-ε2△u+V(|x|)u=W(|x|)up, u>0, u∈H1(RN), with N≥1, ε>0 and p>1. As ε→0, we prove the existence of positive radially symmetric solutions concentrating simultaneously on k spheres. The radii are localized near non-degenerate critical points of the function Γ(r)=rN−1[V(r)]p+1/p−1−1/2[W(r)]−2/p−1.
nonlinear Schrödinger equation,, radial solutions,, spike-layer solutions,, multi-peak solutions,, variational methods.,
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【期刊论文】Infinitely many solutions for p-Laplacian equation
彭双阶
J. Funct. Anal., 262(2012), 2861-2902,-0001,():
-1年11月30日
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【期刊论文】An elliptic equation with combined critical Sobolev-Hardy terms
彭双阶, Wenliang Gaoa, , Shuangjie Pengb, *
Nonlinear Analysis 65(2006)1595-1612,-0001,():
-1年11月30日
Let Ω be a bounded domain in RN (N≥3) with the origin 0 ∈Ω, μ<((N-2)/2)2, 2*(s)=2(N-s)/(N-2); K(x)≥0 and Q(x)≥0 are two smooth functions on Ω. In this paper, we investigate the singular elliptic equation-△u=μu/|x|2+K(x)u2*(s)−1/|x|s+Q(x)u2*(t)−1/|x−x0|t+f(x,u) with Dirichlet boundary conditions. We study the limit behavior of the (P.S.) sequence of the corresponding energy functional and give a global compactness theorem, and then give some existence results.
Sobolev-Hardy terms, Compactness
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【期刊论文】Segregated and synchronized vector solutions for nonlinear
彭双阶
Arch. Ration. Mech. Anal.,2013,-0001,():
-1年11月30日
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【期刊论文】Positive solutions for some singular critical growth nonlinear elliptic equations
彭双阶, Daomin Caoa, , Xiaoming He a, Shuangjic Peng b, c, *
Nonlinear Analysis 60(2005)589-609,-0001,():
-1年11月30日
Let Ω be a bounded domain in RN (N≥4) withsmoothboundary ∂Ω and the origin 0 ∈,μ<((N−2)/2)2, 2*=2N/(N−2), K(x) is a smoothfunction on Ω and positive somewhere.We obtain existence results of positive solutions to the Dirichlet problem −△u=μu/|x|2 +K(x)|u|2*−2u+f(x,u)on Ω, u=0 on ∂Ω for various K(x) and suitable number μ.
Positive solutions, Compactness, Critical Sobolev exponents, Hardy inequality, Singular elliptic equation
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