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1.
Successive iterations for unique positive solution of a nonlinear fractional q-integral boundary value problem
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Guotao Wang Zhanbing Bai Lihong Zhang 《Journal of Applied Analysis & Computation》2019,9(4):1204-1215
In this paper, under certain nonlinear growth conditions, we investigate the existence and successive iterations for the unique positive solution of a nonlinear fractional $q$-integral boundary problem by employing hybrid monotone method, which is a novel approach to nonlinear fractional $q$-difference equation. This paper not only proves the existence of the unique positive solution, but also gives some computable explicit hybrid iterative sequences approximating to the unique positive solution. 相似文献
2.
韦忠礼 《应用泛函分析学报》2011,13(3):274-284
第一部分,介绍分数阶导数的定义和著名的Mittag—Leffler函数的性质.第二部分,利用单调迭代方法给出了具有2序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性和唯一性.第三部分,利用上下解方法和Schauder不动点定理给出了具有2序列Riemann—Liouville分数阶导数微分方程周期边值问题解的存在性.第四部分,利用Leray—Schauder不动点定理和Banach压缩映像原理建立了具有n序列Riemann—Liouville分数阶导数微分方程初值问题解的存在性、唯一性和解对初值的连续依赖性.第五部分,利用锥上的不动点定理给出了具有Caputo分数阶导数微分方程边值问题,在超线性(次线性)条件下C310,11正解存在的充分必要条件.最后一部分,通过建立比较定理和利用单调迭代方法给出了具有Caputo分数阶导数脉冲微分方程周期边值问题最大解和最小解的存在性. 相似文献
3.
田元生 《应用泛函分析学报》2012,14(3):274-281
应用凸锥上的不动点定理,讨论了一类分数阶微分方程m点边值问题正解的存在性,得到了这类边值问题至少存在一个正解的充分条件,并给出了一个实例. 相似文献
4.
Yang Liu 《Applied Mathematics Letters》2012,25(11):1986-1992
In this work, by means of the fixed point theorem in a cone, we establish the existence result for a positive solution to a kind of boundary value problem for a nonlinear differential equation with a Riemann–Liouville fractional order derivative. An example illustrating our main result is given. Our results extend previous work in the area of boundary value problems of nonlinear fractional differential equations [C. Goodrich, Existence of a positive solution to a class of fractional differential equations, Appl. Math. Lett. 23 (2010) 1050–1055]. 相似文献
5.
We are concerning here with the existence of at least one positive continuous solution of coupled systems of quadratic integral equations of fractional orders. Then an existence theorem for a coupled system of Cauchy problems will be proved. 相似文献
6.
The main purpose of this paper is to present the existence results of solutions and positive solutions of nonlinear high-order fractional boundary value problems with integral boundary condition. By using the Banach fixed point theorem and the Krasnosel’skii fixed point theorem, we obtain the existence and uniqueness of real solution. By the Guo–Krasnosel’skii fixed point theorem on the cone, we obtain a desired result for guaranteeing the existence of positive solution. Several interesting examples relevant to the main results are also considered. 相似文献
7.
This paper is devoted to the problem of existence of positive solution for a delay differential equation with fractional order.
Some sufficient conditions for its existence of positive solution are given.
This work was supported in part by the Key Project of the National Nature Science Foundation of China (No. 60534020), the
National Nature Science Foundation of China (No. 60474037), and Program for New Century Excellent Talents in University (No.
NCET-04-415). 相似文献
8.
In this paper, we study the existence of positive solution for the p-Laplacian equations with fractional critical nonlinearity ■where s ∈(0, 1), ps~*=(Np)/(N-sp), N > sp, p > 1 and V(x), K(x) are positive continuous functions which vanish at infinity, f is a function with a subcritical growth, and P(x) is bounded, nonnegative continuous function. By using variational method in the weighted spaces, we prove the above problem has at least one positive solution. 相似文献
9.
10.
Positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator
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Wei Cheng Jiafa Xu Donal O Regan Donal O''Regan Yujun Cui 《Journal of Applied Analysis & Computation》2019,9(5):1959-1972
In this paper using the monotone iterative technique we establish the existence and uniqueness of positive solutions for a nonlinear discrete fractional boundary value problem with a $p$-Laplacian operator. Also we discuss an iterative sequence which yields the approximate solution for this problem. 相似文献
11.
In this paper, we establish the existence result of solution and positive solution for two-point boundary value problem of a semilinear fractional differential equation
by using the Leray-Schauder fixed-point theorem. The discussion is based on the system of integral equations on a bounded region. 相似文献
12.
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative Dαo+is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results. 相似文献
13.
In this work, we consider the uniqueness of positive solutions for fractional differential equation boundary value problems. Our results can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it. 相似文献
14.
Zhanbing Bai 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(2):916-1725
In this paper, we investigate the existence and uniqueness of positive solutions for a nonlocal boundary value problem of fractional differential equation. Firstly, we give Green’s function and prove its positivity; secondly, the uniqueness of positive solution is obtained by the use of contraction map principle and some Lipschitz-type conditions; thirdly, by means of the fixed point index theory, we obtain some existence results of positive solution. The proofs are based upon the reduction of the problem considered to the equivalent Fredholm integral equation of second kind. 相似文献
15.
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. 相似文献
16.
Shuqin Zhang 《Positivity》2012,16(1):177-193
In this paper, we consider the existence of positive solution to some class of singular boundary value problem for fractional
differential equation with nonlinearity that changes sign, our analysis rely on the fixed point index theory. 相似文献
17.
一类次线性分数微分方程的正解存在性 总被引:2,自引:0,他引:2
证明了一类非线性项受幂函数控制的次线性分数微分方程的正解存在性.主要方法是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用.我们的结论表明该方程可以具有一个正解,只要非线性项在某个有界集上的“高度”是适当的. 相似文献
18.
In this paper, we study the existence of positive solutions for a class of higher-order nonlinear fractional differential equations with integral boundary conditions and a parameter. By using the properties of the Green’s function, u 0-positive function and the fixed point index theory, we obtain some existence results of positive solution under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The method of this paper is a unified method for establishing the existence of multiple positive solutions for a large number of nonlinear differential equations of arbitrary order with any allowed number of non-local boundary conditions. 相似文献
19.
运用Schauder不动点定理和上下解方法研究了一类分数阶p-Laplacian边值问题正解的存在性和唯一性,并给出了唯一解的迭代序列. 相似文献
20.
Rongqiang Tang Xinsong Yang Chen Xu Jianwen Feng Fuad E. Alsaadi Tasawar Hayat 《Journal of Applied Mathematics and Computing》2018,56(1-2):289-300
In this paper, we establish sufficient conditions for the existence of positive solutions for a class of higher order Riemann–Liouville fractional initial value problems. First, we construct an appropriate Banach space and prove the equivalence between the posed problem and the associated Volterra integral equation, then by means of Guo–Krasnoselskii fixed point theorem, we investigate the existence of at least one positive solution under sublinearity conditions. 相似文献