非线性发展方程非局部初值问题解的存在性

本文讨论非线性方程的非局部初值问题，利用半群理论、单调算子理论以及Banach不动点定理，分别得到两个问题的温和解和弱解的存在唯一性定理．     

On the existence of positive radial solutions for a certain class of elliptic BVPs

The aim of this paper is to answer the question, when a certain BVP of elliptic type possesses positive radial solutions. We develop duality and variational principles for this problem. Our approach enables the approximation of solutions and gives a measure of a duality gap between primal and dual functional for minimizing sequences.     

二阶三点边值问题正解的存在性

利用锥拉伸和压缩不动点定理,得到了二阶非线性三点边值问题u″（t）＋a（t）u’（t）＋b（t）u（t）＋h（t）f（t,u,（t））=0,t∈（0,1）u（O）=βu（δη）,u（1）=au（η）的正解存在性的充分条件,其中α,β∈[0,＋∞）,0〈η〈1     

On the Existence and Stability of Positive Solutions for Some Pairs of Differential Equations

In this paper, we are concerned with the existence and stability of the positive solutions of a semilinear elliptic system - Δu(x) = a(x)v^6(x) + e(x) - Δv(x) = b(x}u^μ(x) + m(x) \qquad in Ω u = v = 0 \qquad\qquad on ∂Ω where Ω ⊂ R^N is a bounded domain with smooth boundary ∂Ω. It is shown that under the suitable conditions on \delta, μ, there exist a stable and an unstable positive solutions for this system if e and m are sufficiently small in L^∞.     

二阶P—Laplacian问题三个正解的存在性

本文要讨论了二阶P—Laplaci!an方程边值问题{△（φ（Au（t-1）））＋a（t）,（t,u（t））=0,t∈N[1,T＋1];△u（O）=0,u（T＋2）=0三个正解的存在性。通过利用一个三解不动点定理,证明了当,（t,x）在满足较弱条件时该方程至少三个正解的存在性。     

分数阶p-Laplacian Kirchhoff型问题正解的存在性

研究了分数阶p-Laplacian Kirchhoff方程,运用变分法和截断函数理论,证明了在一定条件下具有消失Kirchhoff项的分数阶p-Laplacian问题正解的存在性和多重性.     

具p-Laplacian算子型三点边值问题的正解存在性

本文讨论了一类具有p-Laplacian算子型三点边值问题(Φ_p(y′))′ a(t)f(y)=0,y′(0)=0,y(1)-βy(η)=b,其中Φ_p(y)=│y│~(p-2)y,p>1,且b>0,0<β,η<1.通过使用不动点指数定理,在适当的条件下,建立了关于此类边值问题正解存在性的几个结论。     

分数阶微分方程积分边值问题多个正解的存在性

研究了带有积分边值条件的分数阶微分方程的边值问题.利用LeggettWilliams不动点定理,以及一些分析技巧得到了这类分数阶微分方程边值问题多个正解的存在性.     

非局部边值条件下一类四阶问题的正解

本文研究一类非局部边值条件下非线性项含有二阶导数的四阶问题.利用一个特殊锥上的不动点指数理论,在非线性项满足关联谱半径的一些不等式条件时,获得该问题正解存在的结果.给出了具有变号系数多点形式和变号核积分形式的混合边值条件下的两个例子来说明理论结果的应用.     

三阶非线性奇异边值问题正解存在性

研究三阶奇异边值问题-x=f(t,x,x,′x)″,t∈(0,1),x(0)=x(′0)=x(′1)=0,其中f:(0,1)×(0,∞)×R×R→R连续,f在x=0,t=0与t=1处具有奇性.通过运用上下解方法和单调逼近理论,得到了该问题新的正解的存在性结果.     

有脉冲影响的中立型时滞Lotka-Volterra系统的正周期解的存在性

利用迭合度理论的相关内容,讨论得到了有脉冲影响的中立型时滞Lotka-Volterra系统的正周期解存在的充分条件.     

On the existence of multiple solutions for a nonlocal BVP with vector-valued response

The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.     

关于三阶边值问题解的存在性

利用上下解方法 ,分别讨论了当f∶[0 ,1 ]×R→R在有限区间和无限区间上满足某些增长性条件时 ,三阶微分方程边值问题u (t) +f(t,u) =0 ,u(0 ) =u(1 ) =u″(0 ) =0解与正解的存在性 .最后给出两个例子作为对所获得结果的应用     

奇异非线性p-Laplacian算子方程正解的存在性

通过应用范数形式的锥拉伸与压缩不动点定理,一类含有一维P—Laplacian算子的奇异非线性四点边值问题的正解的存在性被考查,尽管非线性项含有未知函数的一阶导数。     

Bifurcation of Positive Solutions for a Nonlocal Problem

In this paper, we study bifurcation of positive solutions for a nonlocal problem in a bounded domain. Using the degree argument and variational method, we obtain two results about bifurcation of positive solutions.     

一类推广的干摩擦问题周期解的存在性

为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k~2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.     

Asymptotic Solution of a Boundary-Value Problem for Linear Singularly-Perturbed Functional Differential Equations Arising in Optimal Control Theory

The Hamiltonian boundary-value problem, associated with a singularly-perturbed linear-quadratic optimal control problem with delay in the state variables, is considered. A formal asymptotic solution of this boundary-value problem is constructed by application of the boundary function method. The justification of this asymptotic solution is done. The asymptotic solution of the Hamiltonian boundary-value problem is constructed and justified assuming boundary-layer stabilizability and detectability.     

Existence of positive solution for a system of elliptic equations via bifurcation theory

In this paper we study the existence of solution for the following class of elliptic systems

(P)$\{\begin{array}{c}?\mathrm{\Delta }u=(a?{\int }_{\mathrm{\Omega }}K(x,y)f(u,v)dy)u+bv,\text{in}\mathrm{\Omega }\hfill \\ ?\mathrm{\Delta }v=(d?{\int }_{\mathrm{\Omega }}\mathrm{\Gamma }(x,y)g(u,v)dy)v+cu,\text{in}\mathrm{\Omega }\hfill \\ u=v=0,\text{on}?\mathrm{\Omega }\hfill \end{array}$

where $\mathrm{\Omega }?{\mathbb{R}}^N$ is a smooth bounded domain, $N\ge 1$, and $K,\mathrm{\Gamma }:\mathrm{\Omega }\times \mathrm{\Omega }\to \mathbb{R}$ are nonnegative functions satisfying some hypotheses and $a,b,c,d\in \mathbb{R}$. The functions f and g satisfy some conditions which permit to use Bifurcation Theory to prove the existence of solution for (P).