FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].

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.

FIXED POINT INDEX OF UNIFORM LIMIT OF SET-VALUED STRICT SET-CONTRACTIVE MAPPINGS AND ITS APPLICATIONS

In this paper, the class of uniform limit mappings of set-valued, strick set-contractive mappings is discussed. Furthermore, the fixed point index theory for the uniform limit mappings is established. Using the fixed point index theory, some positive fixed point theorems are proved. Our theorems generalize some results in [1,4,5,7].

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

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.

POSITIVE SOLUTIONS FOR SINGULAR BVPs ON THE POSITIVE HALF-LINE ARISING FROM EPIDEMIOLOGY AND COMBUSTION THEORY

In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature.

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.

TWO POSITIVE SOLUTIONS TO THREE-POINT SINGULAR BOUNDARY VALUE PROBLEMS

In this article, we consider the existence of two positive solutions to nonlinear second order three-point singular boundary value problem： -u′′（t） = λf（t, u（t）） for all t ∈ （0, 1） subjecting to u（0） = 0 and αu（η） = u（1）, where η ∈ （0, 1）, α ∈ [0, 1）, and λ is a positive parameter. The nonlinear term f（t, u） is nonnegative, and may be singular at t = 0, t = 1, and u = 0. By the fixed point index theory and approximation method, we establish that there exists λ＊ ∈ （0, ＋∞], such that the above problem has at least two positive solutions for any λ ∈ （0, λ＊） under certain conditions on the nonlinear term f.

EXISTENCE OF A COOPERATIVE ELLIPTIC SYSTEM INVOLVING PUCCI OPERATOR

The authors study the existence of solutions for the nonlinear elliptic system {-Mλ＋,（D2u）=f（u,v）in Ω,-Mλ＋,（D2u）=g（u,v）inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution （u, v）.

MULTIPLE POSITIVE SOLUTIONS FOR SUPERLINEAR SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH DERIVATIVE DEPENDENCE

The existence of at least two positive solutions is presented for the singular second-order boundary value problem{1/p（t）（ p（t）x′（t））′＋Φ（t）f（t,x（t）,p（t）x′（t））=0,0〈t〈1, limt→0 p（t）x′（t）=0,x（1）=0by using the fixed point index, where f may be singular at x = 0 and px ′= 0.

Existence of Multiple solutions for semilinear elliptic equations in the annulus

The existence of radial solutions of Δu ＋ λg（｜x｜）f（u） = 0 in annuli with Dirichlet（Dirichlet/Neumann） boundary conditions is investigated.It is proved that the problems have at least two positive radial solutions on any annulus if f is superlinear at 0 and sublinear at ∞.

Existence of Multiple Positive Solutions for Singular Impulsive Boundary Value Problems in Banach Space

In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.

Existence of Multiple Fixed Points for Nonlinear Operators and Applications

In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a 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.

Existence of Multiple Positive Solutions of Discrete Boundary Value Problem

In this paper, we consider the existence of multiple positive solutions of discrete boundary value problem. The theory of fixed point index is used here to derive the existence theorem.

Positive Solutions of Fourth Order Singular Boundary Value Problems

Using fixed point index theory, we study the existence of positive solutionsof the fourth order differential equation with some general boundary conditions, where g(t) is allowed to be singular at t=0 and/or 1. Our results significantly extend and improve many known results even for non-singular cases. An example is given to show how to apply our theorems.

Positive solutions of second-order differential systems with nonhomogeneous boundary conditions

This paper is to investigate the positive solutions of the systems of second-order ordinary differential equations with nonhomogeneous multi-point boundary conditions. By the lower and upper solutions method, Schauder fixed point theorem and fixed point index theory, under certain conditions, it is proved that there exist appropriate regions of parameters in which the problem has at least two, at least one or no positive solution.

EIGENVECTORS OF SYSTEM OF HAMMERSTEIN INTEGRAL EQUATIONS IN BANACH SPACES ANDAPPLICATIONS

In this paper, the author investigates the existence of eigenvectors of system of Hammerstein integral equations in Banach spaces by means of fixed point index theory. He also gives some applications to a system of S turm-Liouville problems of ordinary differential equations.

Positive solutions of singular superlinear fourth order boundary value problem

The cone theorem and the fixed point index are used to investigate the positive solution of singular superlinear boundary value problem for a fourth order nonlinear differential equation.

Uniqueness of Positive Radial Solutions for a Class of Semipositone Systems on the Exterior of a Ball

In this paper, we study the positive radial solutions for elliptic systems to the nonlinear BVP: , where Δu = div (∇u) and Δv = div (∇v) are the Laplacian of u, λ is a positive parameter, Ω = {x ∈ Rn : N > 2, |x| > r0, r0 > 0}, let i = [1,2] then Ki :[r0,∞] → (0,∞) is a continuous function such that limr→∞ ki(r) = 0 and is The external natural derivative, and : [0, ∞) → (0, ∞) is a continuous function. We discuss existence and multiplicity results for classes of f with a) fi > 0, b) fi < 0, and c) fi = 0. We base our presence and multiple outcomes via the Sub-solutions method. We also discuss some unique findings.