10 papers
A Remark on Attractor Bifurcation
Chunqiu Li, Desheng Li, Jintao Wang
In this paper we present some local dynamic bifurcation results in terms of invariant sets of nonlinear evolution equations. We show that if the trivial solution is an isolated inv…
New Schemes for Solving the Principal Eigenvalue Problems of Perron-like Matrices via Polynomial Approximations of Matrix Exponentials
Desheng Li, Ruijing Wang
A real square matrix is Perron-like if it has a real eigenvalue , called the principal eigenvalue of the matrix, and $\mbox{Re}\,μ<s$ for any other eigenvalue . Nonnegative m…
On Relative Category and Morse Decompositions for Infinite-Dimensional Dynamical Systems
Jintao Wang, Desheng Li
We employ the relative category to develop relations between the Ważewski pair and the Morse decomposition of the maximal invariant set in $\ol{N\sm E}$ for infinite-dimens…
Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities
Desheng Li
This paper is concerned with global estimates and regularity of solutions for the initial value problem of the retarded parabolic equation $$\frac{\patial u}{\patial t}-Δu=f(x,u)+g…
Uniform Decay Estimates for Solutions of a Class of Retarded Integral Inequalities
Desheng Li, Qiang Liu, Xuewei Ju
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,τ)||y_τ||+\int_τ^t K_1(t,s)||y_s||ds+\int_t^\inft…
Equilibrium Index of Invariant Sets and Global Static Bifurcation for Nonlinear Evolution Equations
Desheng Li, Zhi-qiang Wang
We introduce the notion of equilibrium index for statically isolated invariant sets of the system on Banach space (where is a sectorial operator with compa…