Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative

Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends.

A Characterization of the Left Joint Spectrum and Its Applications

In this paper we characterize the left joint spectrum of an n-tuple T = (T1,… ,Tn) of dominant bounded linear operators on a complex Hilbert space H and the unital C-algebra C(T) generated by T1, …,Tn and Ⅰ; moreover, we give an application of this characterization.

On the Existence of Positive Solution for a Nonlinear Third-order Three-point Boundary Value Problem

An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.

Solvability of Third-order Three-point Boundary Value Problems with Caratheodory Nonlinearity

A class of third-order three-point boundary value problems is considered, where the nonlinear term is a Caratheodory function. By introducing a height function and considering the imtegration of this height function, an existence theorem of solution is proved when the limit growth function exists. The main tools are the Lebesgue dominated convergence theorem and the Schauder fixed point theorem.

A Class of Shock Solutions for the Semilinear Singularly Perturbed Boundary Value Problem

The shock solution for the semilinear singularly perturbed two-point boundary value problem was studied. Under suitable conditions and using the theory of differential inequalities, the existence and asymptotic behavior of the solution for the original boundary value problems are discussed. The uniformly effective asymptotic expansion and estimation of solution u(x, ε) were obtained.

Solvability of a class of second-order quasilinear boundary value problems

The second-order quasilinear boundary value problems are considered when the nonlinear term is singular and the limit growth function at the infinite exists. With the introduction of the height function of the nonlinear term on a bounded set and the consideration of the integration of the height function, the existence of the solution is proven. The existence theorem shows that the problem has a solution if the integration of the limit growth function has an appropriate value.

On the growth of transcendental entire functions with multiply connected components

Let g and h be two transcendental entire functions. Suppose that the Fatou set F（goh） contains multiply connected components. In this article, we will consider the growth of the functions g and h.

On the Growth of Transcendental Entire Functions with Unbounded Fatou Components

Suppose that f(z) is a transcendental entire function and that F(f) contains unbounded Fatou components. In this article, we obtained some links between the lower bounds of the lower order of f and the angle of an angular sector which is completely contained in an unbounded Fatou component of F(f). Then, we investigate the bounded components for the Julia set J(f) of a transcendental entire function f(z) and obtain a sufficient and necessary condition.

A Class of Singularly Perturbed Problems for Nonlinear Two-Species Competitive Reaction-Diffusion System

A class of nonlinear two-species competitive singularly perturbed initial-boundary-value problems for reaction-diffusion systems are studied. Under suitable assumptions, by using the stretched variable, the formal asymptotic expansion for the problems is constructed. The uniform validity of the solution for initial-boundary-value problems is obtained by using the theory of differential inequalities.

A Note on a Problem of M. S. Berger

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U (?)E→ F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x)=y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.

Solution and Positive Solution to Nonlinear Cantilever Beam Equations

Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the ＂height＂ of nonlinear term is appropriate on a bounded set.

On the Local Connected and Jordanian Julia Sets

In this article,we investigate the dynamical properties of fλ(z)=λzkez,for λ(≠0)∈C and k≥2.We will show that the boundaries of some (or all) Fatou components are Jordan curves and the Julia sets are Sierpinski carpet,and they are locally connected for some certain λ.

K-Dimension and Hlder Exponent for Bush Type Fractal Functions

Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.

On Relatively Semi-projective and Direct-projective Modules

In this paper, the ＂relative＂ version of semi-projectivity is considered. Let M and N be modules. N is called M-semi-projective, if any homomorphism from N to an M-eyclie submodule f（M） of N can be factored through to a homomorphism from N to M and f, where f∈[M, N]. Some properties of relative semi-projectivity are obtained. Next, we consider a wider class of ＂elatively semi-projective＂ modules such as ＂elatively direct-projective＂ modules which were introduced by Nicholson and Zhou. Several properties of their homomorphisms are also obtained.

Existence,Multiplicity and Infinite Solvability of Positive Solutions for One-Dimensional p-Laplacian

The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.

Triple Positive Periodic Solutions of Nonlinear Singular Second-order Boundary Value Problems

This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u″（t） ＋ λ（t）u（t） = f（t,u（t））,a.e.t ∈ [0,2π],u（0） = u（2π）,u′（0） = u′（2π）,where f（t,u） is a local Carath′eodory function.This shows that the problem is singular with respect to both the time variable t and space variable u.By applying the Leggett-Williams and Krasnosel＇skii fixed point theorems on cones,an existence theorem of triple positive solutions is established.In order to use these theorems,the exact a priori estimations for the bound of solution are given,and some proper height functions are introduced by the estimations.

奇异三阶两点边值问题解的一个存在定理(英文)

由构造合适的 Banach space.an ，存在定理为第三顺序的边界价值问题u'在线性生长的一个条件下面被建立“(t) +f ( t ， u (t)，t'(t)， u ”(t)) =0,0t1 ， u ( 0 )=u'( 0 )=u'( 1 ) =0 ，在非线性的条款包含未知 function.In 的第一和第二衍生物的地方这条定理非线性的条款 f ( t ， u ， v ， w )可能在 t=0 和 t=1.The 单个主要成分 Leray-Schauder 非线性的选择。

Positive Solutions of a Weak Semipositone Third-Order Three-Point Boundary Value Problem

The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″（t）=f（t,u（t））,a.e,t∈[0,1],u（0）=u′（η）=u″（1）=0, where the nonlinear term f（t, u） is a Caratheodory function and there exists a nonnegative function h ∈ L^1[0, 1] such that f（t, u） 〉 ≥-h（t）. The existence of n positive solutions is proved by considering the integrations of ＂height functions＂ and applying the Krasnosel＇skii fixed point theorem on cone.

A(k,n-k) Conjugate Boundary Value Problem with Semipositone Nonlinearity

The existence of positive solution is proved for a （k, n - k） conjugate boundary value problem in which the nonlinearity may make negative values and may be singular with respect to the time variable. The main results of Agarwal et al. （Agarwal R P, Grace S R, O＇Regan D. Semipositive higher-order differential equations. Appl. Math. Letters, 2004, 14： 201-207） are extended. The basic tools are the Hammerstein integral equation and the Krasnosel＇skii＇s cone expansion-compression technique.

New Method for American Options Pricing

A new method using nonlinear regression to approximate the option price based on approximate dynamic programming is proposed. As a result a representation of the American option price is obtained as a solution to the dual minimization problem. In addition, an available Q-value iteration algorithm in practice is given.