8 citations · 19 across the 15 of their papers we have counts for
15 papers
A Note on the Krein-Rutman Theorem for Sectorial Operators
Desheng Li, Ruijing Wang, Luyan Zhou
In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic opera…
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…
Bifurcation from Infinity and Multiplicity of the Landesman-Lazer Type Problem of Elliptic Equations
Xuewei Ju, Desheng Li, Youbin Xiong
This paper deals with the Landesman-Lazer type problem of elliptic equations associated with homogeneous Dirichlet boundary conditions. By using some dynamical arguments we derive…
Global Bifurcation of Dynamical Systems and Nonlinear Evolution Equations
Luyan Zhou, Desheng Li
We establish new global bifurcation theorems for dynamical systems in terms of local semiflows on complete metric spaces. These theorems are applied to the nonlinear evolution equa…
Compactly Generated Shape Index Theory and its Application to a Retarded Nonautonomous Parabolic Equation
Jintao Wang, Jinqiao Duan, Desheng Li
We establish the compactly generated shape (H-shape) index theory for local semiflows on complete metric spaces via more general shape index pairs, and define the H-shape cohomolog…
Local and Global Dynamic Bifurcations of Nonlinear Evolution Equations
Desheng Li, Zhi-Qiang Wang
We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form on a Banach space , where is a sectorial operator,…
Attractors of Local Semiflows on Topological Spaces
Desheng Li, Youbin Xiong, Jintao Wang
In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literatur…
Linking Theorems of Local Semiflows on Complete Metric Spaces
Desheng Li, Guoliang Shi, Xianfa Song
In this paper we prove some linking theorems and mountain pass type results for dynamical systems in terms of local semiflows on complete metric spaces. Our results provide an alte…
Morse Theory of Attractors via Lyapunov Functions
Desheng Li
This paper is concerned with the Morse theory of attractors for semiflows on complete metric spaces. First, we construct global Morse-Lyapunov functions for Morse decompositions of…
Smooth Morse-Lyapunov Functions and Morse Theory of Strong Attractors for Nonsmooth Dynamical Systems
Desheng Li
In this paper we first construct smooth Morse-Lyapunov functions of attractors for nonsmooth dynamical systems. Then we prove that all open attractor neighborhoods of an attractor…