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.

Three-point bending behavior of aluminum foam sandwich with steel panel

Static three-point bending tests of aluminum foam sandwiches with glued steel panel were performed. The deformation and failure of sandwich structure with different thicknesses of panel and foam core were investigated. The results indicate that the maximum bending load increases with the thickness of both steel panel and foam core. The failure of sandwich can be ascribed to the crush and shear damage of foam core and the delamination of glued interface at a large bending load, The crack on the foam wall developed in the melting foam procedure is the major factor for the failure of foam core. The sandwich structure with thick foam core and thin steel panel has the optimal specific bending strength. The maximum bending load of that with 8 mm panel and 50 mm foam core is 66.06 kN.

Breeding of Mycoplasmal pneumonia-negative Swine Population Using Combination Therapy,Segregated Early Weaning(SEW) and Three-point Production System

In order to explore a breeding method for mycoplasmal pneumonia-negative swine population, the purifying effects of combination therapy, SEW and three-point breeding and management system on Mycoplasma hyopneumoniae were investigated in this study. After the processes of screening pregnant sows, programmed therapy for sows, SEW, three-point breeding and management in the barrier isolation system and programmed therapy for piglets, the newly-bred piglets were monitored as long as four months by serum antibody detection of Mycoplasma hyopneumoniae and fluorescent quantitative PCR of nose swabs. The results showed that when the newlybred five batches of piglets were older than 35 d, they were all negative by serum antibody detection and nose swab antigen detection. Therefore, the combination therapy, SEW and three-point production and management system can effectively purify Mycoplasma hyopneumoniae, providing theoretical basis and clinical experience for the control and purification of domestic mycoplasmal pneumonia.

Three-point bending performance of a new aluminum foam composite structure

A new composite structure based on aluminum foam sandwich and fiber metal laminate was proposed. A layer of glass fiber was provided at the interface between the metal panel and the aluminum foam core in this composite structure, using adhesive technology to bond the materials together by organic glue in the sequence of metal panel, glass fiber, aluminum foam core, glass fiber and metal panel. The experimental results show that the new composite structure has an improved comprehensive performance compared with the traditional aluminum foam sandwiches. The optimized parameters for the fabrication of the new aluminum foam composite structure with best bending strength were obtained. The epoxy resin and low porosity aluminum foams are preferred, the thickness of aluminum sheets should be at least 1.5 mm, and the type of glass fiber has little effect on the bending strength. The main failure modes of the new composite structures with two types of glues were discussed.

Three-point bending of honeycomb sandwich beams with facesheet perforations

A novel square honeycomb-cored sandwich beam with perforated bottom facesheet is investigated under threepoint bending,both analytically and numerically.Perforated square holes in the bottom facesheet are characterized by the area ratio of the hole to intact facesheet（perforation ratio）.While for large-scale engineering applications like the decks of cargo vehicles and transportation ships,the perforations are needed to facilitate the fabrication process（e.g.,laser welding）as well as service maintenance,it is demonstrated that these perforations,when properly designed,can also enhance the resistance of the sandwich to bending.For illustration,fair comparisons among competing sandwich designs having different perforation ratios but equal mass is achieved by systematically thickening the core webs.Further,the perforated sandwich beam is designed with a relatively thick facesheet to avoid local indention failure so that it mainly fails in two competing modes：（1）bending failure,i.e.,yielding of beam cross-section and buckling of top facesheet caused by bending moment;（2）shear failure,i.e.,yielding and buckling of core webs due to shear forcing.The sensitivity of the failure loads to the ratio of core height to beam span is also discussed for varying perforation ratios.As the perfo-ration ratio is increased,the load of shear failure increases due to thickening core webs,while that of bending failure decreases due to the weakening bottom facesheet.Design of a sandwich beam with optimal perforation ratio is realized when the two failure loads are equal,leading to significantly enhanced failure load（up to 60%increase）relative to that of a non-perforated sandwich beam with equal mass.

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 Sign-changing Solution for Three-point Boundary Value Problems

In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.

Modified laparoscopic Sugarbaker repair of parastomal hernia with a three-point anchoring technique

AIMTo retrospectively evaluate the safety and feasibility of a new modified laparoscopic Sugarbaker repair in patients with parastomal hernias.METHODSA retrospective study was performed to analyze eight patients who underwent parastomal hernia repair between June 2016 and January 2018. All of these patients received modified laparoscopic Sugarbakerhernia repair treatment. This modifed technique included an innovative three-point anchoring and complete su-turing technique to fix the mesh. All procedures were performed by a skilled hernia surgeon. Demographic data and perioperative outcomes were collected to eva-luate the safety and effcacy of this modifed technique.RESULTSOf these eight patients, two had concomitant incisional hernias. All the hernias were repaired by the modifed laparoscopic Sugarbaker technique with no conversion to laparotomy. Three patients had in-situ reconstruc-tion of intestinal stoma. The median mesh size was 300 cm2, and the mean operative time was 205.6 min. The mean postoperative hospitalization time was 10.4 d, with a median pain score of 1 （visual analog scale method） at postoperative day 1. Two patientsdeveloped postoperative complications. One patient had a pocket of effusion surrounding the biologic mesh, and one patient experienced an infection around the reconstructed stoma. Both patients recovered after conservative management. There was no recurrence during the follow-up period （6-22 mo, average 13 mo）.CONCLUSIONThe modifed laparoscopic Sugarbaker repair could fx the mesh reliably with mild postoperative pain and a low recurrence rate. The technique is safe and feasible for parastomal hernias.

A CATASTROPHE ANALYSIS ON THE STABILITY OF THE CRACK GROWTH IN THREE-POINT BENDING SPECIMENS

This paper presents an attempt at the application of catastrophe theory to the stability analysis of J-controlled crack growth in three-point bending specimens. By introducing the solutions of J-integral in the completely yielding state for the ideal plastic material, the critical condition of losing stability for the crack propagation in the specimen is obtained, based on the cusp catastrophe theory. The process of the crack growth from geometrical sense is described.

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.

Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.

NONTRIVIAL SOLUTION OF A NONLINEAR SECOND-ORDER THREE-POINT BOUNDARY VALUE PROBLEM

In this paper, for a second-order three-point boundary value problem u″＋f（t,u）=0,0〈t〈1,au（0）-bu′（0）=0,u（1）-au（η）=0,where η∈ （0, 1）, a, b, α ∈R with a^2 ＋ b^2 〉 0, the existence of its nontrivial solution is studied. The＇conditions on f which guarantee the existence of nontrivial solution are formulated. As an application, some examples to demonstrate the results are given.

Triple Positive Solutions for a Third-order Three-point Boundary Value Problem

In this paper,we study the existence of triple positive solutions for the nonlinear third-order three-point boundary value problem ■where η∈[0,1/2) is a constant,by using a fixed-point theorem due to Avery and Peterson,we establish results of triple positive solutions to the boundary value problem,and an example is given to illustrate the importance of result obtained.

Existence of Solutions for Second Order Three-Point Boundary Value Problems with Nonlinear Growth

The existence of solutions for second order three-point boundary value problems with nonlinear growth at resonance is studied by using Mawhin continuation theorem. The result shows that theorem 1 and 2 at least have one solution in c1[0,1]

Positive solutions of three-point boundary value problems

In this paper, we consider existence of single or multiple positive solutions of three-point boundary value problems involving one-dimensional p-Laplacian. We then study existence of solutions when the problems are in resonance cases. The proposed approach is based on the Krasnoselskii＇s fixed point theorem and the coincidence degree.

Determination of work-hardening exponent for sheet metal using three-point method

Three characteristic points in the deformation history of a fractured tensile specimen are selected tocalculate two values of n( n1 and n2 ) to represent the hardening ability of material during the homogeneous plas-tic deformation and the following large plastic deformation. Experimental results obtained with mild streel andred copper show that n determined using the three-point method proposed is better to describe the hardening a-bility of material. It is therefore concluded that three-point method can be used to describe the hardening prop-erty of material during both homogeneous deformation and large plastic deformation.

Existence of Multiple Positive Solutions for Third-Order Three-Point Boundary Value Problem

In this paper, we study the existence of positive solutions for a class of third-order three-point boundary value problem. By employing the fixed point theorem on cone, some new criteria to ensure the three-point boundary value problem has at least three positive solutions are obtained. An example illustrating our main result is given. Moreover, some previous results will be improved significantly in our paper.

Triple Positive Solutions to a Third-order Three-point Boundary Value Problem with p-Laplacian Operator

In this paper, we consider the three-point boundary value problem （φp（uˊˊ（t）））ˊ ＋a（t）f（t, u（t）, uˊ（t）, uˊˊ（t）） = 0, t ∈ [0, 1] subject to the boundary conditions u（0） =βuˊ（0）, uˊ（1） = αuˊ（η）, uˊˊ（0） = 0, where φp（s） = ｜s｜p？2s with p 〉 1, 0 〈 α, η 〈 1 and 0 ≤ β 〈 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.

Positive Solutions of a Second-Order Three-point Boundary Value Problem

The existence of positive solutions is established for a nonlinear second-order three-point boundary value problem. The result improves and extends the main result in Electron J. Differential Equations, 34(1999), 1-8.

Three-point explicit compact difference scheme with arbitrary order of accuracy and its application in CFD

Based on the successive iteration in the Taylor series expansion method, a three-point explicit compact difference scheme with arbitrary order of accuracy is derived in this paper. Numerical characteristics of the scheme are studied by the Fourier analysisl Unlike the conventional compact difference schemes which need to solve the equation to obtain the unknown derivatives in each node, the proposed scheme is explicit and can achieve arbitrary order of accuracy in space. Application examples for the convectiondiffusion problem with a sharp front gradient and the typical lid-driven cavity flow are given. It is found that the proposed compact scheme is not only simple to implement and economical to use, but also is effective to simulate the convection-dominated problem and obtain high-order accurate solution in coarse grid systems.