时间标度上的动态方程周期边值问题的正解

讨论了时间标度上一类二阶非线性动态方程的周期边值问题正解以及多解的存在性,利用锥上的不动点理论给出了简捷的判别方法并举例。     

泛函微分方程周期边值问题的正解

讨论一阶泛函微分方程的周期边值问题,利用锥上的不动点定理给出了正解的存在性和多重性的简捷的判别条件.     

On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations

The existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second order ordinary differential equations. The arguments are based only upon the positivity of the Green's functions and the Krasnosel'skii fixed point theorem. As an example, a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity.     

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM

The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.     

非线性四阶周期边值问题正解的存在性和多重性

研究了四阶两参数常微分方程周期边值问题{u（4）（t）-βu″（t）＋αu（t）=f（t,u（τ（t）））,t∈[0,1],u（i）（0）=u（i）（1）,i=1,2,3正解的存在性、多重性和不存在性.在非线性项f（t,u）变号的情形下,用锥上的不动点指数理论证明了该问题至少n个甚至无穷多个正解的存在性,并且获得了该问...     

Structure of positive solution sets of semi-positone singular boundary value problems

In this paper we first obtain some results on the structure of positive solution sets of some differential boundary value problems. Then by using these results we obtain some existence and multiplicity results for positive solutions of differential boundary value problems. The method used to show the main results is that of global bifurcation theories.     

Positive periodic solutions for nonlinear repulsive singular difference equations

The existence and multiplicity of positive solutions are established to the periodic boundary value problems for repulsive singular nonlinear difference equations. The proof relies on a nonlinear alternative of Leray–Schauder type and on Krasnoselskii fixed point theorem on compression and expansion of cones.     

Positive solutions of impulsive boundary value problems for first-order nonlinear functional differential equations

In this paper, we study the problem on the existence of positive solutions for a class of impulsive periodic boundary value problems of first-order nonlinear functional differential equations. By using the fixed point theorem in cones and some analysis techniques, we present some sufficient conditions which guarantee the existence of one and multiple positive solutions for the impulsive periodic boundary value problems. Our results generalize and improve some previous results. Moreover, our results show that positive solutions for the impulsive periodic boundary value problems may be yielded completely by some proper impulsive conditions (see Example 4.1 and Remark 4.2 in Sect. 4), and also implies that proper impulsive conditions are of great significance to simulate processes, optimal control, population model and so on.     

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.     

Multiple positive solutions of the singular boundary value problem for Sturm-Liouville equation with impulses on the half line

We consider the existence of multiple positive solutions of the singular boundary value problem for the Sturm-Liouville equation with impulses on the half line. By applying the fixed-point index theorem of a cone map, existence and multiplicity results about positive solutions are obtained. Our results improve and generalize some well-known results. An example is presented to demonstrate applications of our main results.     

Periodic trajectories with fixed energy on Riemannian and Lorentzian manifolds with boundary

We state some existence and multiplicity results for periodic solutions with prescribed energy of a Lagrangian system and for closed geodesics on Riemannian manifolds convex close to their boundary. As an application we get the existence and multiplicity of periodic trajectories with fixed energy on a class of physically important Lorentzian manifolds with boundary. Entrata in Redazione il 23 aprile 1998. Part of the Ph.D. thesis of this author is contained in this paper. Partially supported by MEC grant PB97-0784-C03-01.     

A global bifurcation phenomenon for second order singular boundary value problems

We establish an existence result of unbounded continuum of solutions from the trivial branch for a second order singular boundary value problem. As an application, we prove several existence and multiplicity results of positive solutions for certain singular boundary value problems.     

二阶非线性常微分方程的正周期解

本文应用Ｋｒａｓｎｏｓｅｌｓｋｉｉ锥映射不动点定理，研究了二阶非线性常微分方程的ω-周期解的存在性，获得了若干正ω-周期解的存在性与多重性结果．     

二阶m点脉冲积-微分方程多个正解的存在性

利用锥上的不动点指数定理讨论了一类二阶m点脉冲积一微分方程边值问题多个正解的存在性,推广和包含了一些已知结果.     

POSITIVE SOLUTIONS TO SINGULAR SECOND ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH SIGN-CHANGING NONLINEARITIES

This paper deals with the existence of positive solutions to the singular secondorder periodic boundary value problem. We obtain the existence results of positive solutions by the fixed point index theory. The results obtained extend and complement some known results.     

Infinitely Many Solutions for Second-Order Quasilinear Periodic Boundary Value Problems with Impulsive Effects

The purpose of this paper is to investigate the multiplicity of solutions for second-order quasilinear periodic boundary value problems with impulsive effects. By using symmetric mountain pass theorem and the genus properties in critical point theory, the existence results of infinitely many solutions are obtained.     

Positive solution for four‐point nonlocal boundary value problems of fractional order

In this paper, we consider the existence of positive solution for four‐point nonlocal boundary value problems of fractional order. By means of some fixed point theorems, some results on the existence and multiplicity of positive solutions are obtained. Furthermore, we provide a representative example to illustrate a possible application of the established results. Copyright © 2013 John Wiley & Sons, Ltd.     

Positive solutions for fractional four-point boundary value problems

In this paper, a fractional four-point boundary value problem is considered. By means of fixed-point theorems and successive iteration method, some results on the existence, multiplicity and uniqueness of positive solutions are obtained.     

Asymptotic analysis of oscillating parametric integrals and ordinary boundary value problems at resonance

This paper deals with boundary value problems whose nonlinear part involves periodic functions and such that the linear part has a one-dimensional solution space. We shall study the existence and multiplicity of solutions using various methods of Nonlinear Analysis such as the Lyapunov-Schmidt reduction and methods of critical point theory. The proofs are based on some general results on the oscillation and asymptotic behavior of certain parametric integrals.     

Multiplicity of positive solutions to period boundary value problems for second order impulsive differential equations

This paper deals with the existence and multiplicity of positive solutions to second order period boundary value problems with impulse effects. The proof of our main results relies on a well-known fixed point theorem in cones. The paper extends some previous results and reports some new results about impulsive differential equations.