本文我们讨论p-Laplace方程-sum from i=1 to n(D_i(∣Du∣^(p-2)D_iu)=u^q+f(x,u)在Neumann边界条件D_Yu=0下的正解存在性,其中1<p<n,g=np/(n-p)-1,f(x,u)为u^q在无穷远点的低阶扰动项。证明了只要(?)f(x,u)/u^(p-1)=α(x)≤0,α...本文我们讨论p-Laplace方程-sum from i=1 to n(D_i(∣Du∣^(p-2)D_iu)=u^q+f(x,u)在Neumann边界条件D_Yu=0下的正解存在性,其中1<p<n,g=np/(n-p)-1,f(x,u)为u^q在无穷远点的低阶扰动项。证明了只要(?)f(x,u)/u^(p-1)=α(x)≤0,α(x)(?)0并且f(x,u)≥-Au^(p-1)-Bu^(t-1)对某正常数A>0,B>0,以及t∈(p-1,n(p-1)/(n-p)),则上述问题存在一个正解。展开更多
Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establ...Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establish the global C^2 estimates and the existence theorem by the method of continuity.展开更多
This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes...This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.展开更多
We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;...We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.展开更多
文摘本文我们讨论p-Laplace方程-sum from i=1 to n(D_i(∣Du∣^(p-2)D_iu)=u^q+f(x,u)在Neumann边界条件D_Yu=0下的正解存在性,其中1<p<n,g=np/(n-p)-1,f(x,u)为u^q在无穷远点的低阶扰动项。证明了只要(?)f(x,u)/u^(p-1)=α(x)≤0,α(x)(?)0并且f(x,u)≥-Au^(p-1)-Bu^(t-1)对某正常数A>0,B>0,以及t∈(p-1,n(p-1)/(n-p)),则上述问题存在一个正解。
基金supported by ZJNSF No. LY17A010022NSFC No.11771396+2 种基金supported by NSFC No. 11471188Wu Wen-Tsun Key Laboratory of Mathematics in USTCsupported by China Scholarship Council
文摘Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establish the global C^2 estimates and the existence theorem by the method of continuity.
文摘This paper deals with the Neumann problem for a class of semilinear elliptic equations -△u + u =|u|2*-2u+ μ|u|q-2u in Ω, au/ar= |u|(?)*-2u on aΩ, where 2 = 2N/N-2, s=2(N-1)/N-2, 1 <q<2,N(?)3,μ>γ denotes the unit outward normal to boundary aΩ. By vaxiational method and dual fountain theorem, the existence of infinitely many solutions with negative energy is proved.
文摘We study the existence of multiple positive solutions for a Neumann problem with singular φ-Laplacian{-(φ（u′）)′= λf（u）, x ∈（0, 1）,u′（0） = 0 = u′（1）,where λ is a positive parameter, φ（s） =s/（1-s;）;, f ∈ C;（[0, ∞）, R), f′（u） > 0 for u > 0, and for some 0 < β < θ such that f（u） < 0 for u ∈ [0, β)（semipositone） and f（u） > 0 for u > β.Under some suitable assumptions, we obtain the existence of multiple positive solutions of the above problem by using the quadrature technique. Further, if f ∈ C;（[0, β） ∪（β, ∞）, R),f′′（u） ≥ 0 for u ∈ [0, β) and f′′（u） ≤ 0 for u ∈（β, ∞）, then there exist exactly 2 n + 1 positive solutions for some interval of λ, which is dependent on n and θ. Moreover, We also give some examples to apply our results.
