Topological degree for 1-set-contractive fields in M-PN spaces and its applications

In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.

THE EXISTENCE AND UNIQUENESS OF TIME-PERIODIC SOLUTIONS TO THE NON-ISOTHERMAL MODEL FOR COMPRESSIBLE NEMATIC LIQUID CRYSTALS IN A PERIODIC DOMAIN

In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.

The Degree Theory of a New Operator

This paper defines a concept of a semi k set contract operator and establishes a degree theory for it.

Existence of Weak Solution for p(x)-Kirchhoff Type Problem Involving the p(x)-Laplacian-like Operator by Topological Degree

In this paper,we study the existence of"weak solution"for a class of p(x)-Kirchhoff type problem involving the p(x)-Laplacian-like operator depending on two real parameters with Neumann boundary condition.Using a topological degree for a class of demicontinuous operator of generalized(S_(+))type and the theory of the variable exponent Sobolev space,we establish the existence of"weak solution"of this problem.

Existence of Multiple Solutions for a Superlinear Sturm Liouville BVPs

The existence of solutions of a Sturm Liouville boundary value problem(BVP) for u″+g(u)=p(t,u,u′)(0≤t≤1) is studied by using a continuation theorem based on the topological degree theory. Under the condition that g grows superlinearly and p grows with respect to u and u′ linearly at most, the boundary value problem has an infinitude of solutions.

EXISTENCE OF POSITIVE SOLUTION FOR A TWO-PATCHES COMPETITION SYSTEM WITH DIFFUSION AND TIME DELAY AND FUNCTIONAL RESPONSE

By using the continuation theorem of coincidence theory, the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional responsex [FK(W1*3/4。*2/3]′ 1 (t)=x 1(t)a 1(t)-b 1(t)x 1(t)-c 1(t)y(t)1+m(t)x 1(t)+D 1(t)[x 2(t)-x 1(t)], x [FK(W1*3/4。*2/3]′ 2 (t)=x 2(t)a 2(t)-b 2(t)x 2(t)-c 2(t)∫ 0 -τ k(s)x 2(t+s) d s+D 2(t)[x 1(t)-x 2(t)], y′(t)=y(t)a 3(t)-b 3(t)y(t)-c 3(t)x 1(t)1+m(t)x 1(t)is established, where a i(t),b i(t),c i(t)(i=1,2,3),m(t) and D i(t)(i=1,2) are all positive periodic continuous functions with period w >0, τ is a nonnegative constant and k(s) is a continuous nonnegative function on [- τ ,0].

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH TIME DELAY

The global asymptotic stability for Hopfield neural networks with time delay was investigated, A theorem and two corollaries were obtained, in which the boundedness and differentiability of f(j) on R in some articles were deleted. Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.

POSITIVE PERIODIC SOLUTION OF A NEUTRAL PREDATOR-PREY SYSTEM

In this paper, the existence o f a positive periodic solution to the following neutral predator_prey system (t)=rH(t)1-a 1(t)H(t-τ)+a 2(t-τ)K-α(t)H(t)P(t), (t)=-b(t)P(t)+β(t)H(t)P(t) is studied,in which r,a 2,K and τ are positive constants, and a 1(t ),α(t),b(t) and β(t) are positive continuous functions of period ω .

Some New Fixed Point Theorems in Probabilistic Metric Spaces

In this paper, we introduce the concept of the Z-M-PN space and obtain somenew fixed point theorems in probabilistic metric spaces Meanwhile,some famous fixedpoint theorems are generalized in probabilistic metric spaces, such a.s fixed point theorem of Schauder, Guo's theorem and fixed point theorem of Petryshyn are generalized in Menger PN-space. And fixed point theorem of Altman is also generalized in the Z-M-PN space.

SOME THEOREMS IN THE X-M-PN SPACE

A new concept of the X-M-PN space is introduced, and the acute angle principle in the X-M-PN space is proved. Meanwhile, some new results are obtained.

1-set-contractive perturbations of accretive operators in Menger PN-spaces

Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

SOLUTIONS FOR SUPERLINEAR(n-1,1)CONJUGATE BOUNDARY VALUE PROBLEMS

The author investigates the existence of positive and nontrivial solutions for superlinear (n - 1, 1) conjugate boundary value problems by means of topological degree theory and cone theory. The main theorems improve some results published recently.

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

Existence and uniqueness of periodic solutions for forced Liénard-type equations

By using topological degree theory and some analysis skill, some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced Lienard-type equations are obtained.

Admissible Periodic Bouncing Solutions for A Class of Semi-linear and Non-conservative Impact Oscillators

In this paper, by using the topological degree method and some limiting arguments, the existence of admissible periodic bouncing solutions for a class of non-conservative semi-linear impact equations is proved.

Nonrecurrence Theorems of Periodic Solutions for Functional Differential Equations

nonrecurrence theorem on the existence of periodic solutions for functional differential equations is proved by employing the topological method, and some applications are given.

The Existence of Periodic Orbits to a Higher Dimensional Autonomous System with aNon-hyperbolic Singular Point *

By means of theory of topological degree in nonlinear functional analysiscombining with qualitative analysis in ordinary differential equations, we discuss theexistence of nontrivial periodic orbits to a higher dimensional autonomous system witha non-hyperbolic singular point.

PBVP of Integrodifferential Equations with Carathéodory Functions

We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.