If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t...If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （...In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.展开更多
In this paper, by using the idea of category, we investigate how the shape of the graph of h（x） affects the number of positive solutions to the following weighted nonlinear elliptic system： = （ N-2-2a 2. where 0 ...In this paper, by using the idea of category, we investigate how the shape of the graph of h（x） affects the number of positive solutions to the following weighted nonlinear elliptic system： = （ N-2-2a 2. where 0 is a smooth bounded domain in ]1N （N 〉 3）, A, cr 〉 0 are parameters, 0 ≤ μ 〈 μa a 2 ＇ h（x）, KI（X） and K2（x） are positive continuous functions in , 1 〈 q 〈 2, a, β 〉 1 and a ＋ β = 2＊（a,b） （2＊ （a, b） 2N = N-2（1＋a-b） is critical Sobolev-Hardy exponent）. We prove that the system has at least k nontrivial nonnegative solutions when the pair of the parameters （）, r） belongs to a certain subset of N2.展开更多
The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and...The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.展开更多
基金the National Natural Science Foundation of China(No.10674024)
文摘If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
基金The project supported by the Natural Science Foundation of Zhejiang Province under Grant No. Y604106, the Foundation of New Century 151 Talent Engineering of Zhejiang Province, the Scientific Research Foundation of Key Discipline of Zhejiang Province, and the Natural Science Foundation of Zhejiang LishuiThe authors are in debt to Profs. J.F. Zhang, Z.M. Sheng, and L.Q. Chen, Drs. Z.Y. Ma and W.H. Huang for their helpful suggestions and fruitful discussions, and express their sincere thanks to Prof. S.Y. Lou for his useful references.University under Grant No. KZ05010
文摘In this paper, the extended projective approach, which was recently presented and successfully used in some continuous nonlinear physical systems, is generalized to nonlinear partial differential-difference systems （DDEs）, As a concrete example, new families of exact solutions to the （2＋1）-dimensional Toda lattice system are obtained by the extended projective approach.
文摘In this paper, by using the idea of category, we investigate how the shape of the graph of h（x） affects the number of positive solutions to the following weighted nonlinear elliptic system： = （ N-2-2a 2. where 0 is a smooth bounded domain in ]1N （N 〉 3）, A, cr 〉 0 are parameters, 0 ≤ μ 〈 μa a 2 ＇ h（x）, KI（X） and K2（x） are positive continuous functions in , 1 〈 q 〈 2, a, β 〉 1 and a ＋ β = 2＊（a,b） （2＊ （a, b） 2N = N-2（1＋a-b） is critical Sobolev-Hardy exponent）. We prove that the system has at least k nontrivial nonnegative solutions when the pair of the parameters （）, r） belongs to a certain subset of N2.
文摘The Nagumo equation ut = △u+ bu(u-a)(1-u), t＞0is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the 'pathological' property of the fractal. However, it is shown that a global Holder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl's formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.
