In this paper,we prove that a composition operator on H^P(B)is Fredholm if and only if it is invertible if and only if its symbol is an automorphism on B,and give the representation of the spectra of a class of compos...In this paper,we prove that a composition operator on H^P(B)is Fredholm if and only if it is invertible if and only if its symbol is an automorphism on B,and give the representation of the spectra of a class of composition operators.In addition,using composition operator,we discuss intertwining Toeplitz operators.展开更多
本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,s...本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,sum from i=1 to m-3βiηi=1.这时dimKer L=2.当βi取不同的符号 时,应用Mawhin重合度定理,证明了多点边值问题的一些存在性结果. 以前文章所 涉及的多点边值问题解的存在性都是在dim Ker L=1的情况下讨论的,所以我们的 工作是新的探索.展开更多
In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the comple...In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.展开更多
We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordi...We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.展开更多
运用Mawhin重合度理论,讨论一类半直线上三阶多点边值问题{x″′(t)=f(t,x(t),x′(t),x″(t))+e(t),t∈[0,+∞),x(0)=m∑i=1α_(i)x(ξ_(i)),x(1)=n∑j=1β_(j)x(η_(j)),limt→+∞x′(t)=∑k=1lγkx″(ζk)在dim Ker L=3共振情形下解...运用Mawhin重合度理论,讨论一类半直线上三阶多点边值问题{x″′(t)=f(t,x(t),x′(t),x″(t))+e(t),t∈[0,+∞),x(0)=m∑i=1α_(i)x(ξ_(i)),x(1)=n∑j=1β_(j)x(η_(j)),limt→+∞x′(t)=∑k=1lγkx″(ζk)在dim Ker L=3共振情形下解的存在性,f:[0,1]×R→R满足S-Carathéodory条件,e∈L1[0,∞),α_(i),β_(j),γk∈R,0<ξ1<ξ2<…<ξm<+∞,0<η1<η2<…<ηn<+∞,0<ζ_(1)<ζ_(2)<…<ζ_(l)<+∞(m,n,l∈Z^(+)),并且满足下列条件:(C1)m∑i=1α_(i)=1,m∑i=1α_(i)ξi=0,m∑i=1α_(i)ξ2i=0,∑j=1nβ_(j)=1,∑j=1nβ_(j)η_(j)=1,∑j=1nβ_(j)η2j=1,∑k=1lγk=1;(C2)Δ=∣∣∣∣Q_(1)e−tQ_(1)te−tQ_(1)t2e−tQ_(2)e−tQ_(2)te−tQ_(2)t2e−tQ_(3)e−tQ_(3)te−tQ_(3)t2e−t∣∣∣∣:=∣∣∣∣a_(11)a_(21)a_(31)a_(12)a_(22)a_(32)a_(13)a_(23)a_(33)∣∣∣∣≠0,其中,Q_(1)y=m∑i=1α_(i)∫ξi_(0)∫^(s)_(0)∫^(τ)_(0)y(v)dv dτds,Q_(2)y=∑j=1nβ_(j)∫^(η_(j))_(0)∫^(s)_(0)∫^(τ)_(0)y(v)dv dτds,Q_(3)y=l∑k=1γk∫^(+∞)_(γk)y(s)ds。展开更多
In this paper,we study composition operators on a Banach space of analytic functions, denoted by X,which includes the Bloch space.This space arises naturally as the dual space of analytic functions in the Bergman spac...In this paper,we study composition operators on a Banach space of analytic functions, denoted by X,which includes the Bloch space.This space arises naturally as the dual space of analytic functions in the Bergman space L_a^1(D)which admit an atomic decomposition.We charac- terize the functions which induce compact composition operators and those which induce Fredholm operatorson this space.We also investigate when a composition operator has a closed range.展开更多
By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete...By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.展开更多
文摘In this paper,we prove that a composition operator on H^P(B)is Fredholm if and only if it is invertible if and only if its symbol is an automorphism on B,and give the representation of the spectra of a class of composition operators.In addition,using composition operator,we discuss intertwining Toeplitz operators.
文摘本文讨论多点边值问题x"(t)=f(t,x(t),x'(t))+e(t),t∈(0,1);x'(0)= x'(ξ),x(1)=sum from i=1 to m-3βix(ηi)解的存在性,其中βi∈R,sum from i=1 to m-3β=1,0<η1<η2< …<ηm-3<1,0<ξ<1,sum from i=1 to m-3βiηi=1.这时dimKer L=2.当βi取不同的符号 时,应用Mawhin重合度定理,证明了多点边值问题的一些存在性结果. 以前文章所 涉及的多点边值问题解的存在性都是在dim Ker L=1的情况下讨论的,所以我们的 工作是新的探索.
文摘In the present paper, the characterization of invertible composition oper-ators on compact Riemann surfaces is obtained, which is very different from that in the case of Hardy or Bergman spaces on a disk of the complex plane C.
基金the National Natural Science Foundation of China(Grant Nos.10325102,10531010)the National Basic Research Program of China(Grant No.2006CB805903)Teaching and Research Award Program for Outstanding Young Teachers,Ministry of Education of China(2001)
文摘We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.
文摘运用Mawhin重合度理论,讨论一类半直线上三阶多点边值问题{x″′(t)=f(t,x(t),x′(t),x″(t))+e(t),t∈[0,+∞),x(0)=m∑i=1α_(i)x(ξ_(i)),x(1)=n∑j=1β_(j)x(η_(j)),limt→+∞x′(t)=∑k=1lγkx″(ζk)在dim Ker L=3共振情形下解的存在性,f:[0,1]×R→R满足S-Carathéodory条件,e∈L1[0,∞),α_(i),β_(j),γk∈R,0<ξ1<ξ2<…<ξm<+∞,0<η1<η2<…<ηn<+∞,0<ζ_(1)<ζ_(2)<…<ζ_(l)<+∞(m,n,l∈Z^(+)),并且满足下列条件:(C1)m∑i=1α_(i)=1,m∑i=1α_(i)ξi=0,m∑i=1α_(i)ξ2i=0,∑j=1nβ_(j)=1,∑j=1nβ_(j)η_(j)=1,∑j=1nβ_(j)η2j=1,∑k=1lγk=1;(C2)Δ=∣∣∣∣Q_(1)e−tQ_(1)te−tQ_(1)t2e−tQ_(2)e−tQ_(2)te−tQ_(2)t2e−tQ_(3)e−tQ_(3)te−tQ_(3)t2e−t∣∣∣∣:=∣∣∣∣a_(11)a_(21)a_(31)a_(12)a_(22)a_(32)a_(13)a_(23)a_(33)∣∣∣∣≠0,其中,Q_(1)y=m∑i=1α_(i)∫ξi_(0)∫^(s)_(0)∫^(τ)_(0)y(v)dv dτds,Q_(2)y=∑j=1nβ_(j)∫^(η_(j))_(0)∫^(s)_(0)∫^(τ)_(0)y(v)dv dτds,Q_(3)y=l∑k=1γk∫^(+∞)_(γk)y(s)ds。
文摘In this paper,we study composition operators on a Banach space of analytic functions, denoted by X,which includes the Bloch space.This space arises naturally as the dual space of analytic functions in the Bergman space L_a^1(D)which admit an atomic decomposition.We charac- terize the functions which induce compact composition operators and those which induce Fredholm operatorson this space.We also investigate when a composition operator has a closed range.
基金Supported by the National Natural Science Foundation of China(No.10171044)the Natural Science Foundation of Jiangsu Province(No.BK2001024)the Foundation for University Key Teachers of the Ministry of Education of China
文摘By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.
