本文对f(x,u)=|z(?)|u|^(p-1)u(l∈R^1,p>1)和f(x,u)=-λ(?)+sum from j=1 to m(A,|x|(?)u(?)),+A|x|^(?)u^P(λ,l_j,P_j,A_j,A,l,P都是常数)证明了半线性椭圆边值问题—△_u=f(x,u),u|(?)=0的k-波节解的唯一性和正解的唯一性,其中Ω...本文对f(x,u)=|z(?)|u|^(p-1)u(l∈R^1,p>1)和f(x,u)=-λ(?)+sum from j=1 to m(A,|x|(?)u(?)),+A|x|^(?)u^P(λ,l_j,P_j,A_j,A,l,P都是常数)证明了半线性椭圆边值问题—△_u=f(x,u),u|(?)=0的k-波节解的唯一性和正解的唯一性,其中Ω={x∈R^N| |x|<R≤+∞}。展开更多
本文主要讨论了R^n中超线性椭圆方程边值问题的k-node解的唯一性,在条件 p1(n)<-(ι+2)/(p-1)<p_2(n)下证明了其k-node解的唯一性,这里p_1(n),P_2(n)是二次方程t(n-2+t)-1=0的根,ι∈R′,p>1,同时给出了 -△u+a(|x|)u=sum from...本文主要讨论了R^n中超线性椭圆方程边值问题的k-node解的唯一性,在条件 p1(n)<-(ι+2)/(p-1)<p_2(n)下证明了其k-node解的唯一性,这里p_1(n),P_2(n)是二次方程t(n-2+t)-1=0的根,ι∈R′,p>1,同时给出了 -△u+a(|x|)u=sum from t=1 to m a_i(|x|)|u|p^(i-1)u,u→0 (|x|→∞)的k-node解的唯一性结果。展开更多
In this paper,we consider the existence of multiple solutions of biharmonic equations boundarv value problem:where Ωis a bounded smooth domain in RN,N ≥ 5;λ∈ R1is a given constant; p = is the critlcal Sobolev expo...In this paper,we consider the existence of multiple solutions of biharmonic equations boundarv value problem:where Ωis a bounded smooth domain in RN,N ≥ 5;λ∈ R1is a given constant; p = is the critlcal Sobolev exponent for the embedding H20 (Ω) → Lp(Ω);△2=△△ denotes iterated N -dimensional Laplacian; f(x) is a given function. Some results about the existence and nonexistence of multiple solutions for problem (1) have been obtained by Ekeland,s variational principle and Mountain-Pass Lemma under some assnmptions on f(x) and N.展开更多
In this paper,we study the following Schrodinger-Poisson system with critical growth:■We establish the existence of a positive ground state solution and a least energy sign-changing solution,providing that the nonlin...In this paper,we study the following Schrodinger-Poisson system with critical growth:■We establish the existence of a positive ground state solution and a least energy sign-changing solution,providing that the nonlinearity f is super-cubic,subcritical and that the potential V(x)has a potential well.展开更多
文摘本文对f(x,u)=|z(?)|u|^(p-1)u(l∈R^1,p>1)和f(x,u)=-λ(?)+sum from j=1 to m(A,|x|(?)u(?)),+A|x|^(?)u^P(λ,l_j,P_j,A_j,A,l,P都是常数)证明了半线性椭圆边值问题—△_u=f(x,u),u|(?)=0的k-波节解的唯一性和正解的唯一性,其中Ω={x∈R^N| |x|<R≤+∞}。
文摘本文主要讨论了R^n中超线性椭圆方程边值问题的k-node解的唯一性,在条件 p1(n)<-(ι+2)/(p-1)<p_2(n)下证明了其k-node解的唯一性,这里p_1(n),P_2(n)是二次方程t(n-2+t)-1=0的根,ι∈R′,p>1,同时给出了 -△u+a(|x|)u=sum from t=1 to m a_i(|x|)|u|p^(i-1)u,u→0 (|x|→∞)的k-node解的唯一性结果。
文摘In this paper,we consider the existence of multiple solutions of biharmonic equations boundarv value problem:where Ωis a bounded smooth domain in RN,N ≥ 5;λ∈ R1is a given constant; p = is the critlcal Sobolev exponent for the embedding H20 (Ω) → Lp(Ω);△2=△△ denotes iterated N -dimensional Laplacian; f(x) is a given function. Some results about the existence and nonexistence of multiple solutions for problem (1) have been obtained by Ekeland,s variational principle and Mountain-Pass Lemma under some assnmptions on f(x) and N.
基金supported by the National NaturalScience Foundation of China(12071170,11961043,11931012,12271196)supported by the excellent doctoral dissertation cultivation grant(2022YBZZ034)from Central China Normal University。
文摘In this paper,we study the following Schrodinger-Poisson system with critical growth:■We establish the existence of a positive ground state solution and a least energy sign-changing solution,providing that the nonlinearity f is super-cubic,subcritical and that the potential V(x)has a potential well.
