Existence and multiplicity of positive solutions for an elastic beam equation

This paper investigates the boundary value problem for elastic beam equation of the form

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.     

非齐次边值条件下一类静态梁方程非负解的存在性

运用Schauder不动点定理，在非齐次边值条件，讨论带导数项的一端简单支撑另一端滑动的静态梁方程y^(4)(x)=f(x,y(x),y′(x),y″，y^(3)（x）），x∈[0,1] y(0)=a,y′（1）＝b,y″（0)=c,y^(3)（1）＝d非负解的存在性，其中a≥0，b≥0，c≤0,d≤0。假定f在零点次线性增长，在无穷远点超线性增长，则上述非齐次边值问题当max{a,b,-c,-d}充分小时有非负解存在，当max{a,b,-c,-d}充分大时无非负解存在。     

An existence theorem of positive solutions for elastic beam equation with both fixed end-points

Abstract. By using the degree theory on cone an existence theorem of positive solution for aclass of fourth-order two-point BVP‘s is obtained. This class of BVP‘s usually describes the de-formation of the elastic beam with both fixed end-points.     

Existence and iteration of positive solutions for a three-point boundary value problem of second order integro-differential equation with p-Laplace operator

In the paper, we obtain the existence of positive solutions and establish a corresponding iterative scheme for the following three-point boundary value problem $$\left\{\begin{array}{l}(\phi_p(u'))'(t)+q(t)f\left(u(t),u'(t),Tu(t),Su(t)\right)=0,\quad0 < t< 1,\\u'(0)=\alpha u'(\eta),\quad u(1)=g(u'(1)),\end{array}\right.$$ where ? _p (s)=|s| ^p?2 s,p>1,α∈[0,1),η∈(0,1), T and S are all linear operators, g(t) is continuous and nonincreasing on (?∞,0]. The main tools are monotone iterative technique and numerical simulation. We illustrate our results by one example, and give its numerical results by iterative scheme.     

Existence and non-existence of positive solutions of BVPs for fractional order elastic beam equations with a non-Caratheodory nonlinearity

In this article, the existence and non-existence results on positive solutions of two classes of boundary value problems for nonlinear singular fractional order elastic beam equations is established. Here f depends on x  x^′$x^{\prime }$ and x^″,f$x^{″}\text{,}f$ may be singular at t=0$t=0$ and t=1$t=1$ and f may be a non-Caratheodory function. The analysis relies on the well known Schauder’s fixed point theorem. By applying iterative techniques, results on the existence of positive solutions are obtained and the iterative scheme which starts off with zero function for approximating the solution is established. The iterative scheme obtained is very useful and feasible for computational purpose. Examples and their numerical simulation are presented to illustrate the main theorems. A conclusion section is also given at the end of this paper.     

Existence of positive solutions of fractional‐order elastic beam equation with a non‐Carathéodory nonlinearity

In this article, the existence of positive solutions of a boundary value problem for nonlinear singular fractional‐order elastic beam equation is established. Here, f depends on t,x, and x′; f may be singular at t = 0 and t = 1; and f is a non‐Carathéodory function. The results obtained are based upon fixed‐point theorems in a cone in Banach space. An example is included to illustrate the main results. Copyright © 2015 John Wiley & Sons, Ltd.     

Infinitely many solutions for a fourth-order elastic beam equation

Existence results of infinitely many solutions for a fourth-order nonlinear boundary value problem are established. No symmetric condition on the nonlinear term is assumed. The main tool is an infinitely many critical points theorem.     

Existence and iteration of positive pseudo-symmetric solutions for a three-point second-order -Laplacian BVP

In this work, we apply a monotone iterative procedure to prove the existence of positive pseudo-symmetric solutions for a three-point second-order p-Laplacian boundary value problem.     

Existence of positive periodic solutions for a functional differential equation with a parameter

In this paper, we study the existence, multiplicity and nonexistence of positive ω$\omega$-periodic solutions for a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones. Some new results are obtained. As an application of our results, we discuss the existence of a positive periodic solution for a class of models of blood cell production with a parameter, which has not been investigated by using previous methods.     

Existence of maximal and minimal solutions to a boundary value problem for the equation of the bending of an elastic beam

By introducing a partial order and using the Mönch fixed point theorem, we establish the existence of maximal and minimal solutions in Banach spaces to a boundary value problem for the equation of the bending of an elastic beam.     

一类弹性梁方程的正解存在性

利用Schauder不动点定理,讨论了两端简单支撑的静态梁方程 y^(4)(x)=f(x,y(x)),y(0)=a,y(1)=b,y“(0)=c,y“(1)=d在非齐边界条件下正解的存在性结果。     

Positive solutions for a beam equation on a nonlinear elastic foundation

Positive solutions for a fourth-order differential equation with nonlinear boundary conditions modeling beams on elastic foundations are considered. The results are shown by using variational methods and a maximum principle for fourth-order equations.     

Twin monotone positive solutions to a singular nonlinear third-order differential equation

This paper discusses the existence of at least one or two nondecreasing positive solutions for the following singular nonlinear third-order differential equation