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91.
Xiuwen Li Zhenhai Liu C. C. Tisdell 《Mathematical Methods in the Applied Sciences》2017,40(12):4548-4559
The aim of this paper is to deal with the existence of mild solutions and exact controllability for a class of fractional evolution inclusions with damping (FEID, for short) in Banach spaces. Firstly, we provide the representation of mild solutions for FEID by applying the method of Laplace transform and the theory of (α,κ)‐regularized families of operators. Next, we are concerned with the existence and exact controllability of FEID under some suitable sufficient conditions by using the method of measure of noncompactness and an appropraite fixed point theorem. Finally, an application to nonlinear partial differential equations with temporal fractional derivatives is presented to illustrate the effectiveness of our main results. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
92.
On the mixed problem for the semilinear Darcy‐Forchheimer‐Brinkman PDE system in Besov spaces on creased Lipschitz domains 下载免费PDF全文
Robert Gutt Mirela Kohr Sergey E. Mikhailov Wolfgang L. Wendland 《Mathematical Methods in the Applied Sciences》2017,40(18):7780-7829
The purpose of this paper is to study the mixed Dirichlet‐Neumann boundary value problem for the semilinear Darcy‐Forchheimer‐Brinkman system in L p ‐based Besov spaces on a bounded Lipschitz domain in , with p in a neighborhood of 2. This system is obtained by adding the semilinear term | u | u to the linear Brinkman equation. First, we provide some results about equivalence between the Gagliardo and nontangential traces, as well as between the weak canonical conormal derivatives and the nontangential conormal derivatives. Various mapping and invertibility properties of some integral operators of potential theory for the linear Brinkman system, and well‐posedness results for the Dirichlet and Neumann problems in L p ‐based Besov spaces on bounded Lipschitz domains in (n ≥3) are also presented. Then, using integral potential operators, we show the well‐posedness in L 2‐based Sobolev spaces for the mixed problem of Dirichlet‐Neumann type for the linear Brinkman system on a bounded Lipschitz domain in (n ≥3). Further, by using some stability results of Fredholm and invertibility properties and exploring invertibility of the associated Neumann‐to‐Dirichlet operator, we extend the well‐posedness property to some L p ‐based Sobolev spaces. Next, we use the well‐posedness result in the linear case combined with a fixed point theorem to show the existence and uniqueness for a mixed boundary value problem of Dirichlet and Neumann type for the semilinear Darcy‐Forchheimer‐Brinkman system in L p ‐based Besov spaces, with p ∈(2?ε ,2+ε ) and some parameter ε >0. 相似文献
93.
Existence of multiplicity harmonic and subharmonic solutions for second‐order quasilinear equation via Poincaré‐Birkhoff twist theorem 下载免费PDF全文
In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second‐order quasilinear equation where , g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase‐plane analysis methods and a generalized version of the Poincaré‐Birkhoff twist theorem. 相似文献
94.
In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone. 相似文献
95.
Shoukry El-Ganaini 《Journal of the Egyptian Mathematical Society》2017,25(1):19-27
In this paper, the first integral method combined with Liu's theorem is applied to integrate a new coupled nonlinear Schrodinger type equation. Using this combination, more new exact traveling wave solutions are obtained for the considered equation using ideas from the theory of commutative algebra. In addition, more solutions are also obtained via the application of semi-inverse variational principle due to Ji-Huan He. The used approaches with the help of symbolic computations via Mathematica 9, may provide a straightforward effective and powerful mathematical tools for solving nonlinear partial differential equations in mathematical physics. 相似文献
96.
In this paper, we will use the Schwarz lemma at the boundary to character the distortion theorems of determinant at the extreme points and distortion theorems of matrix on the complex tangent space at the extreme points for normalized locally biholomorphic quasi-convex mappings in the unit ball B n respectively. 相似文献
97.
Let f(z) be a meromorphic function in the complex plane, whose zeros have multiplicity at least k + 1(k ≥ 2). If sin z is a small function with respect to f(z), then f~(k)(z)-P(z) sin z has infinitely many zeros in the complex plane, where P(z) is a nonzero polynomial of deg(P(z)) ≠ 1. 相似文献
98.
Wen Qiang Shen 《数学学报(英文版)》2017,33(12):1587-1596
In this paper, we generalize Rees–Shishikura’s theorem to the class of geometrically finite rational maps. 相似文献
99.
100.
微分达布定理表明区间内的导函数具有介值性,这使得我们在考虑一些数学分析问题时,往往可以不需要最高阶导函数的连续性.而在微分方程理论中,比较定理的思想对于解的估计非常重要.本文利用比较定理的思想将中值定理类问题转化为微分方程解的估计问题,对于在数学分析的学习中提高学生的认识和兴趣很有意义. 相似文献