共查询到20条相似文献,搜索用时 0 毫秒
1.
Qing Liu 《Mathematical Methods in the Applied Sciences》2012,35(11):1356-1364
In this paper, we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of mild solutions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
2.
This paper is concerned with a nonlocal dispersal population model with spatial competition and aggregation. We establish the existence and uniqueness of positive solutions by the method of coupled upper-lower solutions. We obtain the global stability of the stationary solutions. 相似文献
3.
Yong-Kui Chang V. Kavitha M. Mallika Arjunan 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5551-5559
In this paper, we prove some existence and uniqueness of mild solutions for a semilinear integrodifferential equation of fractional order with nonlocal initial conditions in α-norm. We assume that the linear part generates a noncompact analytic semigroup. Our results cover the cases that the nonlinearity F takes values in different spaces such as X,Xα and Xβ, where α≤β(0,1). Finally, some practical consequences are also obtained. 相似文献
4.
Yongxiang Li 《Journal of Mathematical Analysis and Applications》2009,349(1):226-1324
This paper deals with the existence and uniqueness for the periodic boundary value problem of the semilinear evolution equation in a Hilbert space H
5.
对资产发展方程进行研究,利用非线性分析中的正算子理论和偏微分方程的估计方法,证明了资产发展方程强解的存在惟一性以及资产存量关于科技进步、劳动力函数等因素的单调增结论。 相似文献
6.
Considerable work has gone into studying the properties of nonlocal diffusion equations. The existence of a principal eigenvalue has been a significant portion of this work. While there are good results for the existence of a principal eigenvalue equations on a bounded domain, few results exist for unbounded domains. On bounded domains, the Krein–Rutman theorem on Banach spaces is a common tool for showing existence. This article shows that generalized Krein–Rutman can be used on unbounded domains and that the theory of positive operators can serve as a powerful tool in the analysis of nonlocal diffusion equations. In particular, a useful sufficient condition for the existence of a principal eigenvalue is given. 相似文献
7.
In this paper we investigates the blow-up properties of the positive solutions to a porous medium equation with nonlocal reaction source and with nonlocal boundary condition, we obtain the blow-up condition and its blow-up rate estimate. 相似文献
8.
Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem
obtained is very general and complements previous known results.
The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory
for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714). 相似文献
9.
Existence of the mild solution for some fractional differential equations with nonlocal conditions 总被引:1,自引:0,他引:1
We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential
equation with nonlocal conditions: D
q
x(t)=Ax(t)+t
n
f(t,x(t),Bx(t)), t∈[0,T], n∈ℤ+, x(0)+g(x)=x
0, where 0<q<1, A is the infinitesimal generator of a C
0-semigroup of bounded linear operators on a Banach space X. 相似文献
10.
利用卷积的性质和schauder不动点原理等技巧,在L_(1,i)空间中证明了一类广义Tjon-Wu方程Cauchy问题强解的存在唯一性以及稳态解的存在性. 相似文献
11.
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13.
Giovanni Anello 《Journal of Mathematical Analysis and Applications》2011,373(1):248-1852
We study the uniqueness of solution for the following boundary value problem involving a nonlocal equation of Kirchhoff type
14.
George Bluman Alexei F. Cheviakov 《Journal of Mathematical Analysis and Applications》2007,333(1):93-111
The nonlinear wave equation utt=(c2x(u)ux) arises in various physical applications. Ames et al. [W.F. Ames, R.J. Lohner, E. Adams, Group properties of utt=x[f(u)ux], Int. J. Nonlin. Mech. 16 (1981) 439-447] did the complete group classification for its admitted point symmetries with respect to the wave speed function c(u) and as a consequence constructed explicit invariant solutions for some specific cases. By considering conservation laws for arbitrary c(u), we find a tree of nonlocally related systems and subsystems which include related linear systems through hodograph transformations. We use existing work on such related linear systems to extend the known symmetry classification in [W.F. Ames, R.J. Lohner, E. Adams, Group properties of utt=x[f(u)ux], Int. J. Nonlin. Mech. 16 (1981) 439-447] to include nonlocal symmetries. Moreover, we find sets of c(u) for which such nonlinear wave equations admit further nonlocal symmetries and hence significantly further extend the group classification of the nonlinear wave equation. 相似文献
15.
Ioan I. Vrabie 《Transactions of the American Mathematical Society》2002,354(8):3181-3205
The main goal of the present paper is to define the solution operator associated to the evolution equation , , where generates a -semigroup in a Banach space , , , and to study its main properties, such as regularity, compactness, and continuity. Some necessary and/or sufficient conditions for the compactness of the solution operator extending some earlier results due to the author and to BARAS, HASSAN, VERON, as well as some applications to the existence of certain generalized solutions to a semilinear equation involving distributed, or even spatial, measures, are also included. Two concrete examples of elliptic and parabolic partial differential equations subjected to impulsive dynamic conditions on the boundary illustrate the effectiveness of the abstract results. 相似文献
16.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(7):2245-2251
We discuss the existence of positive solutions of a nonlocal boundary value problem that models a chemical tubular reactor. Our approach allows us to deal with a wide range of parameters, nonlocal conditions and to provide upper and lower bounds for the solutions. We make use of the theory of fixed point index for compact maps. Some examples are presented to illustrate the theory. 相似文献
17.
In the paper, we study the positive solutions of an elliptic system coming from a preypredator model with modified Leslie-Gower
and Holling-Type II schemes. We study the existence, non-existence, bifurcation, uniqueness and stability of positive solutions.
In particular, we obtain a continuum of positive solutions connecting a semi-trivial solution to the unique positive solution
of the limiting system.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10471022, 10771032) and Natural Science
Foundation of Jiangsu Province (Grant No. BK2006088) 相似文献
18.
Blow-up and lifespan of solutions to a nonlocal parabolic equation at arbitrary initial energy level
We consider a nonlocal parabolic equation. By exploiting the boundary condition and the variational structure of the equation, we prove finite time blow-up of the solution for initial data at arbitrary energy level. We also obtain the lifespan of the blow-up solution. The results generalize the former studies on this equation. 相似文献
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20.
Xinfu Chen 《Journal of Differential Equations》2005,212(1):62-84
We consider entire solutions of ut=uxx-f(u), i.e. solutions that exist for all (x,t)∈R2, where f(0)=f(1)=0<f′(0). In particular, we are interested in the entire solutions which behave as two opposite wave fronts of positive speed(s) approaching each other from both sides of the x-axis and then annihilating in a finite time. In the case f′(1)>0, we show that such entire solution exists and is unique up to space-time translations. In the case f′(1)<0, we derive two families of such entire solutions. In the first family, one cannot be any space-time translation of the other. Yet all entire solutions in the second family only differ by a space-time translation. 相似文献