In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, ...In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.展开更多
This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic g...This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.展开更多
In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be un- bounded by making use of the M...In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be un- bounded by making use of the Morse theory for a C^2-function at both isolated critical point and infinity.展开更多
基金NSFC!( 1 9671 0 1 7) and NSF!( A970 1 2 ) of Fujian.
文摘In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.
基金supported by the National Natural Science Foundation of China(Nos.11631004,12031009).
文摘This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.
文摘In this paper we study the existence of nontrivial solutions of a class of asymptotically linear elliptic resonant problems at higher eigenvalues with the nonlinear term which may be un- bounded by making use of the Morse theory for a C^2-function at both isolated critical point and infinity.
