FIXED POINT INDEX THEORY FOR WEAKLY INWARD MAPPINGS

In this paper we define a fixed point index theory for locally Lip., completely continuous and weakly inward mappings defined on closed convex sets in general Banach spaces where no other artificial conditions are imposed. This makes ns to deal with these kinds of mappings more easily. As obvious applications, some results in [3],[5],[7],[9],[10] are deepened and extended.

Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator

This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results.

FIXED POINTS AND EXPONENTIAL STABILITY OF ALMOST PERIODIC MILD SOLUTIONS TO STOCHASTIC VOLTERRA-LEVIN EQUATIONS

In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic mild solutions to the system.

ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS

In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.

THE RELATION BETWEEN SIGN-CHANGING SOLUTION AND POSITIVE-NEGATIVE SOLUTIONS FOR NONLINEAR OPERATOR EQUATIONS AND ITS APPLICATIONS

By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x = Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.

An Alternative Way of Utilizing Fixed Point Theory

The author proposes an alternative way of using fixed point theory to get the existence for semilinear equations.As an example,a nonlocal ordinary differential equation is considered.The idea is to solve homogeneous equations in the linearization.One feature of this method is that it does not need the equation to have special structures,for instance,variational structures,maximum principle,etc.Roughly speaking,the existence comes from good properties of the suitably linearized equation.The idea may have wider application.

Existence and Uniqueness of Anti-periodic Solutions for 2n-order Differential Equations

In this paper, we study the anti-periodic solutions for 2n-th order differential equations. By using the Schauder＇s fixed point theorem, we present some new results about the existence and uniqueness of anti-periodic solutions for 2n-th order differential equations.

The Existence of Periodic Solutions of a Class of <i>n</i>-Degree Polynomial Differential Equations*

This paper deals with a class of n-degree polynomial differential equations. By the fixed point theorem and mathematical analysis techniques, the existence of one (n is an odd number) or two (n is an even number) periodic solutions of the equation is obtained. These conclusions have certain application value for judging the existence of periodic solutions of polynomial differential equations with only one higher-order term.

ON THE EXISTENCE AND STABILITY OF SOLUTION FOR SEMI－HOMOGENEOUS BOUNDARY VALUE PROBLEM

In this paper. we discuss the existence and stability of solution for two semi-homogeneous boundary value problems. The relative theorems in [1.2] are extended. Meanwhile. we obtain some new results.

Dynamical study of varicella-zoster virus model in sense of Mittag-Leffler kernel

The primary varicella-zoster virus(VzV)infection that causes chickenpox(also known as varicella),spreads quickly among people and,in severe circumstances,can cause to fever and encephalitis.In this paper,the Mittag-Leffler fractional operator is used to examine the mathematical representation of the vzV.Five fractional-order differential equations are created in terms of the disease's dynamical analysis such as S:Susceptible,V:Vaccinated,E:Exposed,I:Infectious and R:Recovered.We derive the existence criterion,positive solution,Hyers-Ulam stability,and boundedness of results in order to examine the suggested fractional-order model's wellposedness.Finally,some numerical examples for the VzV model of various fractional orders are shown with the aid of the generalized Adams-Bashforth-Moulton approach to show the viability of the obtained results.

Least Number of Periodic Points of Self-maps of Lie Groups

There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M → M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g is continuous} and NJDn（f） = min{#Fix（gn）; g - f; g is smooth}. In general, NJDn（f） may be much greater than NFn（f）. If M is a torus, then the invariants are equal. We show that for a self-map of a nonabelian compact Lie group, with free fundamental group, the equality holds 〈=〉 all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.

On Nonnegative Solution of Multi-Linear System with Strong M_(z)-Tensors

A class of structured multi-linear system defined by strong M_(z)-tensors is considered.We prove that the multi-linear system with strong M_(z)-tensors always has a nonnegative solution under certain condition by the fixed point theory.We also prove that the zero solution is the only solution of the homogeneous multi-linear system for some structured tensors,such as strong M-tensors,H^(+)-tensors,strictly diagonally dominant tensors with positive diagonal elements.Numerical examples are presented to illustrate our theoretical results.

EXISTENCE OF POSITIVE SOLUTIONS TO SUBLINEAR SECOND-ORDER PERIODIC BOUNDARY VALUE PROBLEM

In this paper, we consider a second-order periodic boundary value problem. By the topological degree theory and fixed point index theory, we prove the existence of positive solutions which gives the relationship between the first positive eigenvalue of the associated eigenvalue problem and the behavior of the nonlinear term of the system.

Self-maps of S2 Homotopic to a Smooth Map with a Single n-periodic Point

We show for which （d, n） ∈ Z × N there exists a smooth self-map f ： S2 → S2 so that deg（f） = d and Fix（fn） is a point.

Existence and Exponential Stability of Almost Periodic Solution for BAM Neural Networks with Impulse

This paper discusses a class of the bidirectional associative memories（BAM） type neural networks with impulse.By using the Banach fixed point theory and some analysis technology,we obtain the existence of almost periodic solution and stability under some sufficient conditions.

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM FOR ONE-DIMENSIONAL p-LAPLACIAN

We study the existence of positive solutions to boundary value problems for one- dimensional p-Laplacian under some conditions about the first eigenvalues correspon- ding to the relevant operators by the fixed point theory. The main difficulties are the computation of fixed point index and the subadditivity for positively 1-homogeneous operator.

ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS

By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.

ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES

The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved,with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.

EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.

POSITIVE SOLUTIONS TO A CLASS OF SECOND-ORDER SINGULAR SEMIPOSITIVE NEUMANN BOUNDARY VALUE PROBLEM WITH GENERAL FORM

By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded.