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1.
分数阶奇异微分方程初值问题正解的存在性 总被引:3,自引:0,他引:3
分数阶微分方程解的存在性问题近年来引起了许多人的关注,本文考察了一个非线性分数阶奇异微分方程初值问题正解的存在性,我们的结果削弱了Babakhani, Varsha的假设条件,并要求其非线性项具有一定程度的奇异性. 相似文献
2.
《数学的实践与认识》2015,(11)
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. 相似文献
3.
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. 相似文献
4.
研究了一类分数阶广义非线性扰动热波方程.首先用奇异慑动方法,求出了分数阶广义非线性扰动热波方程初始边值问题的任意次近似解析解.然后利用泛函分析不动点定理证明了它的一致有效性,最后简述了它的物理意义.求得的近似解析解,弥补了单纯用数值方法求模拟解的不足. 相似文献
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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. 相似文献
7.
李强 《数学物理学报(A辑)》2020,(4):918-924
该文考虑的是带有分数阶耗散项(一△)αu和(-△)βd的广义不可压缩液晶模型.目标是在需要最小的耗散情况下建立整体正则性.在初值充分光滑的情况下,若耗散指标α≥5/4,β≥5/4,方程组有唯一的整体光滑解. 相似文献
8.
在这篇文章, 我们研究了一分数阶基尔霍夫问题, 在一些适当的条件下, 得到了非平凡非负基态解的存在性. 相似文献
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通过研究非线性分数阶微分方程边值问题D_(0+)~αu(t)+y(t,u(t))=0,0相似文献
11.
Zhanbing Bai 《Applied mathematics and computation》2009,215(7):2761-2767
In this paper, we establish the existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation. Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone. 相似文献
12.
Existence of positive solutions to a boundary value problem for a delayed singular high order fractional differential equation with sign-changing nonlinearity
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In this paper, we discuss the existence of positive solutions to the boundary value problem for a high order fractional differential equation with delay and singularities including changing sign nonlinearity. By using the properties of the Green function, Guo-krasnosel"skii fixed point theorem, Leray-Schauder"s nonlinear alternative theorem, some existence results of positive solutions are obtained, respectively. 相似文献
13.
We consider the following nonlinear elliptic equation with singular nonlinearity: where α>β>1, a>0, and Ω is an open subset of , n2. Let uH1(Ω) with and be a nonnegative stationary solution. If we denote the zero set of u by we shall prove that the Hausdorff dimension of Σ is less than or equal to . 相似文献
14.
Marcelo Montenegro Olivâine Santana de Queiroz 《Journal of Differential Equations》2009,246(2):482-511
We study the nonlinear elliptic problem −Δu=χ{u>0}(logu+λf(x,u)) in Ω⊂Rn with u=0 on ∂Ω. The function is nondecreasing, sublinear and fu is continuous. For every λ>0, we obtain a maximal solution uλ?0 and prove its global regularity . There is a constant λ∗ such that uλ vanishes on a set of positive measure for 0<λ<λ∗, and uλ>0 for λ>λ∗. If f is concave, for λ>λ∗ we characterize uλ by its stability. 相似文献
15.
This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type under Navier boundary conditions, \(u=\triangle u=0\). Here \(\varOmega \subset {\mathbf {R}}^N\), \(N\ge 1\) is a bounded \(C^4\)-domain, \(0\in \varOmega \), h(x) and k(x) are positive continuous functions, \(\gamma \in (0,1)\), \(\alpha \in (0,1)\) and \(M:{\mathbf {R}}^+\rightarrow {\mathbf {R}}^+\) is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for \(\lambda > \frac{\mu }{\mu ^*m_0}\) and \(0<\mu <\mu ^*\). Here \(\mu ^*=\Big (\frac{N(N-4)}{4}\Big )^2\) is the best constant in the Hardy inequality. Besides, if \(\mu =0\), \(\lambda >0\) and h, k are Lipschitz functions, we show that this problem has a positive smooth solution. If \(h,k\in C^{2,\,\theta _0}(\overline{\varOmega })\) for some \(\theta _0\in (0,1)\), then this problem has a positive classical solution.
相似文献
$$\begin{aligned} \triangle ^2 u-\lambda M(\Vert \nabla u\Vert ^2)\triangle u-\frac{\mu }{\vert x\vert ^4}u=\frac{h(x)}{u^\gamma }+k(x)u^\alpha , \end{aligned}$$
16.
Existence of solution for a singular critical elliptic equation 总被引:1,自引:0,他引:1
In this paper, a singular semilinear elliptic problem involving the critical Sobolev exponent is studied by variational method, the existence of a solution is proved under certain conditions. The Hardy inequality is used and plays an important role in the discussion. 相似文献
17.
Existence and uniqueness of positive solution for nonlinear fractional q-difference equation with integral boundary conditions
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Caixia Guo Jianmin Guo Shugui Kang Huapeng Li 《Journal of Applied Analysis & Computation》2020,10(1):153-164
This paper studies a class of nonlinear fractional $q$-difference equations with integral boundary conditions. By exploiting the properties of Green"s function and two fixed point theorems for a sum operator, the existence and uniqueness of positive solutions for the boundary value problem are established. Iterative schemes for approximating the solutions are also obtained. Explicit examples are given to illustrate main results. 相似文献
18.
Kang Qun Zhang 《数学学报(英文版)》2012,28(6):1135-1154
In this paper, we study the existence and regularity of a solution to the initial datum problem of a semilinear generalized Tricomi equation in mixed-type domain. We suppose that an initial datum on the degenerate plane is smooth away from the origin, and has a conormal singularity at this point, then we show that in some mixed-type domain, the solution exists and is conormal with respect to the characteristic conic surface which is issued from the origin and has a cusp singularity. 相似文献
19.
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
20.
Zhou Wen-Shu 《Journal of Mathematical Analysis and Applications》2008,346(1):107-119
In this paper we study existence and multiplicity of weak solutions of the homogenous Dirichlet problem for a singular semilinear elliptic equation with a quadratic gradient term. The proofs for the main results are based on a priori estimates of solutions of approximate problems. 相似文献