一类二阶微分议程边值问题三解的存在性

§ 1　 IntroductionWe are interested in the existence ofthree-solutions ofthe following second-order dif-ferential equations with nonlinear boundary value conditionsx″=f( t,x,x′) ,　　 t∈ [a,b] ,( 1 .1 )g1 ( x( a) ,x′( a) ) =0 ,　　 g2 ( x( b) ,x′( b) ) =0 ,( 1 .2 )where f:[a,b]×R1 ×R1 →R1 ,gi:R1 ×R1 →R1 ( i=1 ,2 ) are continuous functions.The study ofthe existence of three-solutions ofboundary value prolems forsecond or-der differential equations was initiated by Amann[1 ] .In[1 …     

Existence of solutions to functional boundary value problem of second-order nonlinear differential equation

In this paper, a functional boundary value problem is studied. Based on Mawhin's coincidence degree theory, some existence theorems are obtained in the case of non-resonance and the cases of and at resonance. The results not only generalize and improve some known results of multi-point and integral boundary value problems, but also give some existence theorems for boundary value problems that all their boundary value conditions are relied on both x and x^′.     

Existence of positive solutions for singular impulsive differential equations with integral boundary conditions

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共振条件下二阶积分边值问题解的存在性（英文）

利用上下解方法和带参数的紧向量场解集的连通性质研究了共振条件下一类二阶微分方程积分边值问题{u′′（t）=f（t,u（t））,t∈（0,1）,u（0）=∫10u（s）dα（s）,u（1）=∫10u（s）dβ（s）解的存在性.     

On a third-order multi-point boundary value problem at resonance

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Positive solutions for fourth-order differential equations with deviating arguments and integral boundary conditions

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Existence result of solutions to differential equations of variable-order with nonlinear boundary value conditions

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Solvability for second-order three-point boundary value problems at resonance on a half-line

This paper deals with the solvability and uniqueness of the second-order three-point boundary value problems at resonance on a half-line

     

共振条件下积分边值问题解的存在性

运用Mawhin重合度理论建立了二阶Stieltjes积分边值问题解的存在性定理,其所得结果推广了多点边值问题已有的一些结论。     

Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained.     

分数阶微分方程耦合系统共振边值问题解的存在性

利用Mawhin迭合度理论,讨论了共振条件下分数阶微分方程耦合系统两点边值问题解的存在性,得到了解的存在性和唯一性的充分条件,最后通过一个例子加以说明.     

Existence of positive solutions for singular ordinary differential equations with nonlinear boundary conditions

We prove the existence of nonnegative solutions of the problem , , for a physically motivated class of nonlinearity . The results, which are established using a ``forbidden value' argument, are new even in the case of linear .

     

Solvability of boundary value problem at resonance for third-order functional differential equations

This paper is devoted to the study of boundary value problem of third-order functional differential equations. We obtain some existence results for the problem at resonance under the condition that the nonlinear terms is bounded or generally unbounded. In this paper we mainly use the topological degree theory.     

一类含非线性边界条件的高阶微分方程解的存在性(英文)

将上下解方法和Leray-Shauder度应用到一类含有非线性边界条件的n阶微分方程,得到了至少存在一个解的结果,并且改进和推广了文献中的某些结果.     

含积分边界条件的分数阶微分方程边值问题的正解的存在性

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Boundary integral equations for bending of thermoelastic plates with transmission boundary conditions

The solution of an initial‐boundary value problem for bending of a piecewise‐homogeneous thermoelastic plate with transverse shear deformation is represented as various combinations of single‐layer and double‐layer time‐dependent potentials. The unique solvability of the boundary integral equations generated by these representations is proved in spaces of distributions. Copyright © 2009 John Wiley & Sons, Ltd.     

Existence for neutral impulsive functional differential equations with nonlocal conditions

In this paper, we study a class of neutral impulsive functional differential equations with nonlocal conditions. We suppose that the linear part satisfies the Hille-Yosida condition on a Banach space and it is not necessarily densely defined. We give some sufficient conditions ensuring the existence of integral solutions and strict solutions. To illustrate our abstract results, we conclude this work by an example.     

Boundary value problem for second-order differential operators with integral conditions

In this article, we study a second-order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two-point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called regular and nonregular cases, we prove that the resolvent decreases with respect to the spectral parameter in L ^p ?(0,?1), but there is no maximal decreasing at infinity for p?>?1. Furthermore, the studied operator generates in L ^p ?(0,?1) an analytic semigroup for p?=?1 in regular case, and an analytic semigroup with singularities for p?>?1 in both cases, and for p?=?1 in the nonregular case only. The obtained results are then used to show the correct solvability of a mixed problem for a parabolic partial differential equation with nonregular boundary conditions.