一类分数阶微分方程多点边值问题解的存在性

本文运用Krasnoselskii和Schauder不动点定理,得到了一类分数阶微分方程多点边值问题解的存在性．     

非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性

本文研究一类非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性,利用一些标准的不动点定理进行证明.     

一类分数阶微分方程边值问题正解的存在性

构建了一格林函数,采用新的分析方法即利用锥拉伸锥压缩不动点定理和Leggett—Williams不动点定理,在较弱的条件下研究了一类分数阶微分方程,得到该问题一个以及多个正解的存在性,使原有结果得到进一步改进,并给出了一个实例．     

一类分数阶微分方程四点边值问题解的存在性

研究了一类分数阶微分方程四点边值问题解的存在性,利用Schauder不动点定理,得到了边值问题至少存在一个解的充分条件.     

一类分数阶差分方程边值问题多重正解的存在性

考虑一类高阶分数阶差分方程边值问题.构造相关的格林函数,利用不等式技巧,分析格林函数的特征性质.运用不动点指数理论,获得了该分数阶差分方程边值问题存在多重正解的充分条件,举例说明了所获理论的有效性.     

一类具有p-Laplacian算子的分数阶差分方程边值问题的正解

该文研究一类具有p-Laplacian算子的分数阶差分方程边值问题.借助离散型Jensen不等式,考虑该问题与相应的不带有p-Laplacian算子的分数阶差分方程边值问题之间的关系,并运用不动点指数理论获得该问题正解的存在性.     

一类具有Riemann-Liouville分数阶积分边值条件的奇异分数阶微分方程解的存在性

研究一类具有Riemann-Liouville分数阶积分边值条件的奇异分数阶微分方程解的存在性,其非线性项包含Caputo型分数阶导数,且在t=0具有奇异性.应用Schauder不动点定理获得了解的存在性定理,并给出了应用实例.     

带有非局部条件分数阶差分方程解的存在性和唯一性

主要考虑如下分数阶差分方程△^vy(t)=-f(t+v-1,y(t+v-1))在非局部条件y(v-2)=ψ(y),y(v+b)=ψ(y)下的边值问题(BVP),其中t∈[0,b],f:[v-1,v,…,v+b-1]_(N_(v-1))×R→R,f为连续函数,(?),ψ∈C(v-2,v+b])→R,1相似文献   

一类分数阶p-Laplacian差分方程边值问题正解的存在性北大核心CSCD

研究一类带p-Laplacian算子的分数阶差分方程边值问题.利用格林函数的特征性质、压缩映射原理及锥上的不动点定理等非线性方法,获得了该分数阶pLaplacian差分方程边值问题解的唯一性及正解的存在性条件,举例说明了所得结论的正确性.     

一类分数阶奇异微分方程积分边值问题正解的存在性

研究一类具有Riemann-Liouville导数的分数阶奇异微分方程积分边值问题的可解性.运用Guo-Krasnoselskii不动点定理,得到了奇异微分方程积分边值问题正解的存在性定理.最后,给出了一个实例,用于说明所得结论的有效性.     

Continuity of Solutions of a Class of Fractional Equations

In practice many problems related to space/time fractional equations depend on fractional parameters. But these fractional parameters are not known a priori in modelling problems. Hence continuity of the solutions with respect to these parameters is important for modelling purposes. In this paper we will study the continuity of the solutions of a class of equations including the Abel equations of the first and second kind, and time fractional diffusion type equations. We consider continuity with respect to the fractional parameters as well as the initial value.     

Asymptotic Behavior of Solutions for a Class of Fractional Integro-differential Equations

In this paper, we study the asymptotic behavior of solutions for a general class of fractional integro-differential equations. We consider the Caputo fractional derivative. Reasonable sufficient conditions under which the solutions behave like power functions at infinity are established. For this purpose, we use and generalize some well-known integral inequalities. It was found that the solutions behave like the solutions of the associated linear differential equation with zero right hand side. Our findings are supported by examples.     

Multiple Nontrivial Solutions for a Class of p-Laplacian Equations

In this paper a class of p-Laplacian equations are considered. The existence of five nontrivial solutions is stated. By the standard supersolution and subsolution method, we prove the existence of minimal positive solution and maximal negative solution in L ^∞(Ω). Furthermore, in virtue of the well-known Mountain-Pass Theorem and Second Deformation Theorem, we can give additional three nontrivial solutions, i.e., one positive solution, one negative solution and one sign-changing solution.     

Multiple Solutions for a Class of Semilinear Elliptic Equations

We show that for a class of semilinear elliptic equations there are at least three nontrivial solutions. Existence of infinitely many solutions is also shown when the nonlinear term is odd. In our results, the nonlinear term can grow super-critically at infinity.

     

非线性差分方程的多重周期解

用变分方法得到一类非线性差分方程多重周期解的存在性．我们的结果推广了Cai，Yu和Guo[Comput．Math．Appl．，52（2006），1630-1647]的结果，并且这里给出的证明显著地简化了．     

一类非线性分数阶发展方程的新精确解

利用exp(-Φ(ξ)展开法,分别得到非线性分数阶Phi-4方程,非线性分数阶foam drainage方程,非线性分数阶SRLW方程的新精确解.实践证明,方法简洁方便,对于研究非线性分数阶发展方程具有十分重要的意义.     

一类非线性微分差分方程的近似解

本文对一类非线性微分差分方程求得一致有效渐近展开式,给出了共振解的近似解析表达式,并推广了Nayfeh和Mook的结果.     

Existence of Solutions to a Class of Fractional Differential Equations

In this paper, the existence of solutions to a class of fractional differential equations $D_{0+}^{\alpha}u(t)=h(t)f(t, u(t), D_{0+}^{\theta}u(t))$ is obtained by an efficient and simple monotone iteration method. At first, the existence of a solution to the problem above is guaranteed by finding a bounded domain $D_M$ on functions $f$ and $g$. Then, sufficient conditions for the existence of monotone solution to the problem are established by applying monotone iteration method. Moreover, two efficient iterative schemes are proposed, and the convergence of the iterative process is proved by using the monotonicity assumption on $f$ and $g$. In particular, a new algorithm which combines Gauss-Kronrod quadrature method with cubic spline interpolation method is adopted to achieve the monotone iteration method in Matlab environment, and the high-precision approximate solution is obtained. Finally, the main results of the paper are illustrated by some numerical simulations, and the approximate solutions graphs are provided by using the iterative method.     

Existence and Properties of Solutions for a Class of Fractional Differential Equations

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we consider the initial value problem of a class of fractional differential equations. Firstly, we obtain the existence and...     

AF—代数的闭的Jordan理想

讨论AF-代数的闭的Jordan理想。我们证明了AF-代灵敏的一个闭的子集是其一Jordan理想的充分必要条件是它是一个结合理想。