In this paper we give the existence of mild solutions for semilinear Cauchy problems u′（t） = Au（t） ＋f（t, u（t））, t ∈ I, a.e. with nonlocal initial condition u（O） = g（u） ＋uo when the map g loses compactn...In this paper we give the existence of mild solutions for semilinear Cauchy problems u′（t） = Au（t） ＋f（t, u（t））, t ∈ I, a.e. with nonlocal initial condition u（O） = g（u） ＋uo when the map g loses compactness in Banach spaces.展开更多
Many authors have studied the limit hehavior of the sequence of probability measureon a topological group or scmigroup.As to the description of the limit behavior of the sequence by the essential point setof the convo...Many authors have studied the limit hehavior of the sequence of probability measureon a topological group or scmigroup.As to the description of the limit behavior of the sequence by the essential point setof the convolution sequence, Maximov studied the case of compact topologica1 group. Inthis note, the problem of weak convergence for the sequence of convolution power of aprobability measure is considered on the locally compact topological semigroup. Jn particu-lar. the relation between the essential point set of the sequence and the support set of theweak limit of the sequence is studied.展开更多
Weak convergence of convolution products of non-identical probability measures on topological semigroups is investigated Firstly, the dependence relationship between the semigroup N of measures and suppN is studied; s...Weak convergence of convolution products of non-identical probability measures on topological semigroups is investigated Firstly, the dependence relationship between the semigroup N of measures and suppN is studied; secondly, a necessary and sufficient condition that insures the strong uniform composition convergence of sequence |μn| is presented; thirdly, a more extensive class of semigroups is found, on which |μn| must be of strong uniform composition convergence, if it is of composition convergence.展开更多
文摘In this paper we give the existence of mild solutions for semilinear Cauchy problems u′（t） = Au（t） ＋f（t, u（t））, t ∈ I, a.e. with nonlocal initial condition u（O） = g（u） ＋uo when the map g loses compactness in Banach spaces.
基金Project supported by the Natural Science Foundation of Shandong Province.
文摘Many authors have studied the limit hehavior of the sequence of probability measureon a topological group or scmigroup.As to the description of the limit behavior of the sequence by the essential point setof the convolution sequence, Maximov studied the case of compact topologica1 group. Inthis note, the problem of weak convergence for the sequence of convolution power of aprobability measure is considered on the locally compact topological semigroup. Jn particu-lar. the relation between the essential point set of the sequence and the support set of theweak limit of the sequence is studied.
基金Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province,China
文摘Weak convergence of convolution products of non-identical probability measures on topological semigroups is investigated Firstly, the dependence relationship between the semigroup N of measures and suppN is studied; secondly, a necessary and sufficient condition that insures the strong uniform composition convergence of sequence |μn| is presented; thirdly, a more extensive class of semigroups is found, on which |μn| must be of strong uniform composition convergence, if it is of composition convergence.
