共查询到20条相似文献,搜索用时 15 毫秒
1.
We discuss the value of the best constant in Gaffney inequality namely when either or on ?Ω. 相似文献
2.
Qiong Liu 《Mathematical Methods in the Applied Sciences》2021,44(1):593-604
By using some real analysis techniques, we study the structural characteristics of a multi‐parameter Hilbert‐type integral inequality with the hybrid kernel and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrate some results of references but also find some new Hilbert‐type integral inequalities with simple form by choosing suitable parameter values. 相似文献
3.
Belen Lpez Juan Rocha Kishin Sadarangani 《Mathematical Methods in the Applied Sciences》2019,42(1):49-58
In this paper, Lyapunov‐type inequalities are derived for a class of fractional boundary value problems with integral boundary conditions. As an application, we obtain a lower bound for the eigenvalues of corresponding equations. 相似文献
4.
5.
We prove the uniqueness for the solutions of the singular nonlinear PDE system:
(1) |
In the special case when and , we classify all the solutions and thus obtain the best constant in the corresponding weighted Hardy-Littlewood-Sobolev inequality.
6.
Hartman–Wintner‐type inequalities for a class of nonlocal fractional boundary value problems 下载免费PDF全文
In this paper, we establish new Hartman–Wintner‐type inequalities for a class of nonlocal fractional boundary value problems. As an application, we obtain a lower bound for the eigenvalues of corresponding equations. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
7.
Jiabin Zuo Tianqing An Alessio Fiscella 《Mathematical Methods in the Applied Sciences》2021,44(1):1071-1085
The paper deals with the following Kirchhoff‐type problem where M models a Kirchhoff coefficient, is a variable s(·) ‐order p(·) ‐fractional Laplace operator, with and . Here, is a bounded smooth domain with N > p(x, y)s(x, y) for any , μ is a positive parameter, g is a continuous and subcritical function, while variable exponent r(x) could be close to the critical exponent , given with and for . We prove the existence and asymptotic behavior of at least one non‐trivial solution. For this, we exploit a suitable tricky step analysis of the critical mountain pass level, combined with a Brézis and Lieb‐type lemma for fractional Sobolev spaces with variable order and variable exponent. 相似文献
8.
K. Watanabe Y. Kametaka K. Takemura 《Journal of Mathematical Analysis and Applications》2008,340(1):699-706
The best constants Cm,j of Sobolev embedding of Hm(0,a) into Cj[0,a](0?j?m−1) are obtained. Especially, when a=∞, these constants can be represented in a closed form. 相似文献
9.
In this paper, we consider a nonhomogeneous space‐time fractional telegraph equation defined in a bounded space domain, which is obtained from the standard telegraph equation by replacing the first‐order or second‐order time derivative by the Caputo fractional derivative , α > 0 and the Laplacian operator by the fractional Laplacian ( ? Δ)β ∕ 2, β ∈ (0,2]. We discuss and derive the analytical solutions under nonhomogeneous Dirichlet and Neumann boundary conditions by using the method of separation of variables. The obtained solutions are expressed through multivariate Mittag‐Leffler type functions. Special cases of solutions are also discussed. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
10.
设1/p=1/q≈1:1且P〉1.通过引入一个适当的积分核函数和参数λ(λ〉-1),创建了一种新型Hardy~Hilbert型积分不等式.证明了其常数因子(p^λ=1+q^λ+1)Г(λ+1)是最佳的,其中Г(x)Г-函数.特别,当p=2时,得到了一种新的Hilbert型积分不等式.作为应用,给出了它的一种等价形式. 相似文献
11.
Milton Ferreira R. Sren Kraußhar M. Manuela Rodrigues Nelson Vieira 《Mathematical Methods in the Applied Sciences》2019,42(10):3633-3653
In this paper, we develop a fractional integro‐differential operator calculus for Clifford algebra‐valued functions. To do that, we introduce fractional analogues of the Teodorescu and Cauchy‐Bitsadze operators, and we investigate some of their mapping properties. As a main result, we prove a fractional Borel‐Pompeiu formula based on a fractional Stokes formula. This tool in hand allows us to present a Hodge‐type decomposition for the fractional Dirac operator. Our results exhibit an amazing duality relation between left and right operators and between Caputo and Riemann‐Liouville fractional derivatives. We round off this paper by presenting a direct application to the resolution of boundary value problems related to Laplace operators of fractional order. 相似文献
12.
Fausto Ferrari 《Mathematische Nachrichten》2006,279(8):815-830
In this note, we prove a Harnack inequality for two‐weight subelliptic p ‐Laplace operators together with an upper bound of the Harnack constant associated with such inequality. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
《Mathematische Nachrichten》2017,290(16):2597-2611
In this paper, we consider the bifurcation problem for the fractional Laplace equation where is an open bounded subset with smooth boundary, stands for the fractional Laplacian. We show that a continuum of solutions bifurcates out from the principal eigenvalue λ1 of the problem and, conversely. 相似文献
14.
Guotao Wang Xueyan Ren Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2020,43(5):2646-2655
The purpose of the current study is to investigate IBVP for spatial-time fractional differential equation with Hadamard fractional derivative and fractional Laplace operator(−Δ)β. A new Hadamard fractional extremum principle is established. Based on the new result, a Hadamard fractional maximum principle is also proposed. Furthermore, the maximum principle is applied to linear and nonlinear Hadamard fractional equations to obtain the uniqueness and continuous dependence of the solution of the IBVP at hand. 相似文献
15.
In this paper, we study decay properties of solutions to the wave equation of p‐Laplacian type with a weak dissipation of m‐Laplacian type. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
《Mathematical Methods in the Applied Sciences》2018,41(7):2733-2747
An inverse problem of determining a time‐dependent source term from the total energy measurement of the system (the over‐specified condition) for a space‐time fractional diffusion equation is considered. The space‐time fractional diffusion equation is obtained from classical diffusion equation by replacing time derivative with fractional‐order time derivative and Sturm‐Liouville operator by fractional‐order Sturm‐Liouville operator. The existence and uniqueness results are proved by using eigenfunction expansion method. Several special cases are discussed, and particular examples are provided. 相似文献
17.
Xindong Zhang Pengzhan Huang Xinlong Feng Leilei Wei 《Numerical Methods for Partial Differential Equations》2013,29(4):1081-1096
In this article, we consider the finite element method (FEM) for two‐dimensional linear time‐fractional Tricomi‐type equations, which is obtained from the standard two‐dimensional linear Tricomi‐type equation by replacing the first‐order time derivative with a fractional derivative (of order α, with 1 <α< 2 ). The method is based on finite element method for space and finite difference method for time. We prove that the method is unconditionally stable, and the error estimate is presented. The comparison of the FEM results with the exact solutions is made, and numerical experiments reveal that the FEM is very effective. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013 相似文献
18.
Juan Bory‐Reyes Marco Antonio Prez‐de la Rosa 《Mathematical Methods in the Applied Sciences》2021,44(1):605-616
The Moisil‐Teodorescu operator is considered to be a good analogue of the usual Cauchy–Riemann operator of complex analysis in the framework of quaternionic analysis and it is a square root of the scalar Laplace operator in . In the present work, a general quaternionic structure is developed for the local fractional Moisil–Teodorescu operator in Cantor‐type cylindrical and spherical coordinate systems. Furthermore, in order to reveal the capacity and adaptability of the methods, we show two examples for the Helmholtz equation with local fractional derivatives on the Cantor sets by making use of the local fractional Moisil–Teodorescu operator. 相似文献
19.
In this paper, we concern with the following fractional p‐Laplacian equation with critical Sobolev exponent where ε > 0 is a small parameter, λ > 0 , N is a positive integer, and N > ps with s ∈ (0, 1) fixed, . Since the nonlinearity does not satisfy the following Ambrosetti‐Rabinowitz condition: with μ > p , it is difficult to obtain the boundedness of Palais‐Smale sequence, which is important to prove the existence of positive solutions. In order to overcome the above difficulty, we introduce a penalization method of fractional p‐Laplacian type. 相似文献