In this paper, we construct the orthogonal wavelet basis in the space of antiperiodic functions by appealing the spline methods. Differing from other results in papers([1,2,3,6,8]), here we derive the 3-scale equation...In this paper, we construct the orthogonal wavelet basis in the space of antiperiodic functions by appealing the spline methods. Differing from other results in papers([1,2,3,6,8]), here we derive the 3-scale equation, by using this equation we construct some basic functions, those functions can be used to construct different orthonormal basis in some spline function spaces.展开更多
This paper is mainly concerned with the S-asymptotically Bloch type periodicity.Firstly,we introduce a new notion of S-asymptotically Bloch type periodic functions,which can be seen as a generalization of concepts of ...This paper is mainly concerned with the S-asymptotically Bloch type periodicity.Firstly,we introduce a new notion of S-asymptotically Bloch type periodic functions,which can be seen as a generalization of concepts of S-asymptoticallyω-periodic functions and S-asymptoticallyω-anti-periodic functions.Secondly,we establish some fundamental properties on S-asymptotically Bloch type periodic functions.Finally,we apply the results obtained to investigate the existence and uniqueness of S-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.展开更多
This paper is concerned with some nonlinear heat equations with initial condition and anti-periodic boundary condition. Also some two-point value nonlinear heat equations with anti-periodic boundary condition are disc...This paper is concerned with some nonlinear heat equations with initial condition and anti-periodic boundary condition. Also some two-point value nonlinear heat equations with anti-periodic boundary condition are discussed. The existence and uniqueness of the solutions are given. Some asymptotic behaviors of the solutions are studied.展开更多
文摘In this paper, we construct the orthogonal wavelet basis in the space of antiperiodic functions by appealing the spline methods. Differing from other results in papers([1,2,3,6,8]), here we derive the 3-scale equation, by using this equation we construct some basic functions, those functions can be used to construct different orthonormal basis in some spline function spaces.
基金supported by NSF of Shaanxi Province(2020JM-183).
文摘This paper is mainly concerned with the S-asymptotically Bloch type periodicity.Firstly,we introduce a new notion of S-asymptotically Bloch type periodic functions,which can be seen as a generalization of concepts of S-asymptoticallyω-periodic functions and S-asymptoticallyω-anti-periodic functions.Secondly,we establish some fundamental properties on S-asymptotically Bloch type periodic functions.Finally,we apply the results obtained to investigate the existence and uniqueness of S-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.
文摘This paper is concerned with some nonlinear heat equations with initial condition and anti-periodic boundary condition. Also some two-point value nonlinear heat equations with anti-periodic boundary condition are discussed. The existence and uniqueness of the solutions are given. Some asymptotic behaviors of the solutions are studied.
