This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a...This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a nonlinear term.Since there are no periodic assumptions on L（t）and W（t,z）in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W（t,z）is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.展开更多
The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regulari...The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.展开更多
In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.
Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weight...Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.展开更多
In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal elem...In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal element theorem.展开更多
Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed modul...Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.展开更多
Local and global existence and uniqueness theorems for a functional delay fractional differential equation with bounded delay are investigated. The continuity with respect to the initial function is proved under Lipsc...Local and global existence and uniqueness theorems for a functional delay fractional differential equation with bounded delay are investigated. The continuity with respect to the initial function is proved under Lipschitz and the continuity kind conditions are analyzed.展开更多
We establish the existence theorem of three nontrivial solutions for a class of semilinear elliptic equation on RN by using variational theorems of mixed type due to Marino and Saccon and linking theorem.
The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and b...The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.展开更多
文摘This paper concerns the existence of multiple homoclinic orbits for the second-order Hamiltonian system-L（t）z＋Wz（t,z）=0,where L∈C（R,RN2）is a symmetric matrix-valued function and W（t,z）∈C1（R×RN,R）is a nonlinear term.Since there are no periodic assumptions on L（t）and W（t,z）in t,one should overcome difficulties for the lack of compactness of the Sobolev embedding.Moreover,the nonlinearity W（t,z）is asymptotically linear in z at infinity and the system is allowed to be resonant,which is a case that has never been considered before.By virtue of some generalized mountain pass theorem,multiple homoclinic orbits are obtained.
基金Supported by the NNSF of China(10771110,11171306)Supported by the the New Century 151 Talent Project of Zhejiang Province
文摘The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.
文摘In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.
文摘Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.
基金the National Natural Science Foundation of China (10171118)the Education Committee project Research Foundation of Chongqing (030801)and the Science Committee project Research Foundation of Chongqing (8409)
文摘In this paper, some existence theorems of a solution for generalized vector quasivariational-like inequalities without any monotonity conditions in a noncompact topological space setting are proven by the maximal element theorem.
文摘研究环的Ore扩张的幂零p.p.性,幂零Baer性和弱Mc Coy性,主要证明了:设R是一个拟IFP和(α,δ)-condition环,则有(1)如果R是幂零p.p.-环,则R[x;α,δ]是幂零p.p.-环;(2)如果R是幂零Baer环,则R[x;α,δ]是幂零Baer环;(3)R[x;α,δ]是右弱M c Coy环。
基金supported by National Natural Science Foundation of China(Grant Nos.11171015 and 11301568)
文摘Let（Ω , E, P） be a probability space, F a sub-σ-algebra of E, L^p（E）（1 p ＋∞） the classical function space and LF^p（E） the L^0（F）-module generated by L^p（E）, which can be made into a random normed module in a natural way. Up to the present time, there are three kinds of conditional risk measures, whose model spaces are L^∞（E）, L^p（E）（1 p ＋∞） and LF^p（E）（1 p ＋∞） respectively, and a conditional convex dual representation theorem has been established for each kind. The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems. We first establish the relation between L^p（E） and LF^p（E）, namely LF^p（E） = Hcc（L^p（E））, which shows that LF^p（E）is exactly the countable concatenation hull of L^p（E）. Based on the precise relation, we then prove that every L^0（F）-convex L^p（E）-conditional risk measure（1 p ＋∞） can be uniquely extended to an L^0（F）-convex LF^p（E）-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter, which shows that the study of L^p-conditional risk measures can be incorporated into that of LF^p（E）-conditional risk measures. In particular, in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L^0-convex conditional risk measures.
基金the Scientific and Technical Research Council of Turkey.
文摘Local and global existence and uniqueness theorems for a functional delay fractional differential equation with bounded delay are investigated. The continuity with respect to the initial function is proved under Lipschitz and the continuity kind conditions are analyzed.
文摘We establish the existence theorem of three nontrivial solutions for a class of semilinear elliptic equation on RN by using variational theorems of mixed type due to Marino and Saccon and linking theorem.
基金Project supported by the National Natural Science Foundation of China (No. 10971194)the Zhejiang Provincial Natural Science Foundation of China (Nos. Y7080008, R6090109)the Zhejiang Innovation Project (No. T200905)
文摘The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems where N ≥ 2, 2 ≤ p ≤ N and F ： R^2 →% is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.
