Assume that 0<p<∞ and that B is a connected nonempty open set in R^(n),and that A^(p)(B)is the vector space of all holomorphic functions F in the tubular domains R^(n)+iB such that for any compact set K⊂B,‖ y...Assume that 0<p<∞ and that B is a connected nonempty open set in R^(n),and that A^(p)(B)is the vector space of all holomorphic functions F in the tubular domains R^(n)+iB such that for any compact set K⊂B,‖ y →‖x →F(x+iy)‖Lp(R^(n))‖ L(K)<∞,so A^(p)(B)is a Frechet space with the Heine-Borel property,its topology is induced by a complete invariant metric,is not locally bounded,and hence is not normal.Furthermore,if 1≤p≤2,then the element F of A^(p)(B)can be written as a Laplace transform of some function f∈L(R^(n)).展开更多
This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the...This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.展开更多
In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.
In this paper, we study the impulsive equation for nonlinear boundary va-lue problem by the monotone iterative method when some of the traditional boundary conditions are violated.
基金This work was partially supported by NSFC(11971045,12071035 and 11971063).
文摘Assume that 0<p<∞ and that B is a connected nonempty open set in R^(n),and that A^(p)(B)is the vector space of all holomorphic functions F in the tubular domains R^(n)+iB such that for any compact set K⊂B,‖ y →‖x →F(x+iy)‖Lp(R^(n))‖ L(K)<∞,so A^(p)(B)is a Frechet space with the Heine-Borel property,its topology is induced by a complete invariant metric,is not locally bounded,and hence is not normal.Furthermore,if 1≤p≤2,then the element F of A^(p)(B)can be written as a Laplace transform of some function f∈L(R^(n)).
基金This work was supported by grants from NNSF of China(No:10271044)Scientific Research Fund of Educational Department of Anhui Province(NSF2003KJ005zd)Teaching Research Fund of Educational Department of Anhui Province(JYXM2003108).
文摘This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.
基金supported by the NSF of Shandong Province (No.2010AL013)
文摘In this paper,we consider the system of Sturm-Liouville singular BVP and present a sufficient and necessary condition for the existence of positive solutions by means of the fixed point theorem for regular cones.
基金Project supported by the National Natural Science Foundation of China (19871048) and the Natural Science Foundation of Shandong
文摘In this paper, we study the impulsive equation for nonlinear boundary va-lue problem by the monotone iterative method when some of the traditional boundary conditions are violated.
