On the Positive Solutions of a Nonlinear Fourth-order Boundary Value Problem with Two Parameters

The existence of m positive solutions is proven for a nonlinear fourth-order boundary value problem with two parameters, where m is an arbitrary natural number. This kind of fourth-order boundary value problems usually describes the equilibrium state of elastic beam where both ends are simply supported. The main ingredient is Krasnosel'skii fixed point theorem of cone expansion–compression type.     

凹泛函型锥拉伸与压缩不动点定理

本文通过凹泛函构造了Banach空间中的一个收缩核,并利用收缩核给出了凹泛函型锥拉伸与压缩不动点定理,扩展和完善了已有文献中的一些结果.     

一类积分方程的五解定理

利用H.Amann的一个不动点定理及锥拉伸锥压缩不动点定理讨论了一类Hammerstein型积分方程的正解,得到了一个五解定理.     

A generalization of the cone expansion and compression fixed point theorem and applications

The classical Krasnosel’skii fixed point theorem concerning cone compression and expansion of norm type is extended; in it the norm is replaced with some convex functional. As an application, the existence of positive solutions for the singular second-order m$m$-point boundary value problem is considered.     

无穷时滞泛函微分方程的正周期解

利用范数形式的锥拉伸和锥压缩不动点定理讨论具有无穷时滞泛函微分方程的周期解问题,获得了正周期解的存在性定理,并给出了定理的若干应用.     

四阶奇异边值问题两个正解的存在性

利用锥拉伸与压缩不动点定理，给出了四阶微分方程奇异边值问题C^2[0，1]和C^2-[0，1]正解的存在性．     

Existence of symmetric positive solutions for a class of Sturm-Liouville-like boundary value problems

This paper deals with the existence of symmetric positive solutions for a class of singular Sturm-Liouville-like boundary value problems with a one-dimensional p-Laplacian operator. By using the fixed theorem of cone expansion and compression of norm type in a cone, the existence of positive solutions is established though nonlinear term contains the first derivative of unknown function.     

非线性三阶微分方程组边值问题的多个正解

本文通过利用范数形式的锥拉伸和压缩不动点定理及Leggett-Williams不动点定理,获得了非线性三阶微分方程组边值问题多个正解的存在性,并给出了一些例子说明结果的应用.     

关于一个新泛函的锥拉伸与锥压缩不动点定理及应用

引进了一个新的泛函,它包含了已有的很多类型的泛函.关于此泛函建立了一个泛函形式的锥拉伸与锥压缩不动点定理,并应用此定理研究了一类二阶两点边值问题,得到了该问题至少一个正解的存在性.     

Existence of Positive Solutions to Fourth Order Quasilinear Boundary Value Problems

In this paper, we generalize the fixed point theorem of cone expansion and compression of norm type to the theorem of functional type. As an application, the existence of positive solutions for some fourth-order beam equation boundary value problems is obtained. The emphasis is put on that the nonlinear term is dependent on all lower order derivatives.     

二阶奇异积分边值问题的正解

By using the fixed point index in cone and the fixed theorem of cone expansion and compression, the existence of positive solutions to the singular second-order boundary value problem is considered.     

Multiple Positive Solutions for First Order Impulsive Singular Integro-Differential Equations on the Half Line

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Multiple positive solutions for first order impulsive superlinear integro-differential equations on the half line

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.     

Symmetric positive solutions for nonlinear boundary value problems with ϕ-Laplacian operator

This paper proves the existence, multiplicity, and nonexistence of symmetric positive solutions to nonlinear boundary value problems with Laplacian operator. We improve and generalize some relative results. Our analysis mainly relies on the fixed point theorem of cone expansion and compression of norm type.     

一类奇异脉冲微分方程周期边值问题的多解性

利用非线性Leray-Schauder二择一定理和锥拉伸与压缩不动点定理,讨论了一类奇异二阶脉冲微分方程在周期边值条件下多个正解的存在性.     

Fixed point theorem of Leggett-Williams type and its application

We establish a norm-type cone expansion and compression fixed point theorem for completely continuous operators. Our theorem is then applied to prove the existence of positive solution of second order three-point boundary value problem.     

On existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system

By employing the fixed point theorem of cone expansion and compression of norm type, we investigate the existence of positive solutions of Sturm-Liouville boundary value problems for a nonlinear singular differential system. Some well-known results in the literature are generalized and improved. An example is presented to illustrate the application of our main result.     

α凸算子(α>1)的正不动点存在性及其应用

通过构造一个特殊的锥,利用锥拉伸与压缩不动点定理对α凸算子(α>1)正不动点的存在性与不可比较性作了研究,并将其结果应用到超线性多项式型Hammerstein积分方程．     

一类非线性四阶边值问题正解的存在性

利用锥拉伸和锥压缩不动点定理和上下解的方法,建立了一类四阶微分方程组奇异边值问题正解存在性与不存在性定理,推广了文[2],[3]的问题,进一步完善了文[2],[3]的相关结果.