共查询到20条相似文献,搜索用时 93 毫秒
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在强连续半群紧和非紧的条件下,使用Schauder不动点定理和Krasnoselselskii不动点定理,分别得到了Banach空间中具有非局部条件的半线性中立型测度方程适度解的存在性. 相似文献
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抽象半线性发展方程初值问题解的存在性 总被引:17,自引:0,他引:17
本文研究Banach空间E中具有非紧半群的半线性发展方程初值问题u′(t)+Au(t)=f(t,u(t)),t≥0;u(0)=x_0解的存在性,其中-A为E中等度连续C_0-半群的生成元,f:[0,∞)×E→E连续。在f满足较弱的非紧性测度条件下,获得了该问题饱和mild解的存在性。特别,当E为有序弱序列完备Banach空间时,我们获得了一个不需要非紧性测度条件的便于应用的存在性结果。 相似文献
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张文丽 《应用泛函分析学报》2012,(2):166-171
在非线性项f是关于u的奇函数,势函数是有界的周期函数且下界是正的,Sobolev嵌入缺乏了紧性和f不再满足(AR)条件下,运用临界点理论中的喷泉定理和集中紧性原则证明了R~N中具有周期势函数的一类超线性p-Laplacian方程存在无穷多非平凡解。 相似文献
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讨论了Banach空间X中带有非局部条件的半线性发展方程.在g失去紧性的条件下,利用L^p(I;X)空间中的不动点定理,对边值问题适度解的存在性做了研究,完善和推广了已有结论.最后给出一个在偏微分方程中的例子. 相似文献
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孟立平 《数学的实践与认识》2012,42(8):218-222
在不假定f满足非紧性测度条件及上下解存在的情形下,用算子谱理论与半序方法获得了有序Banach空间E中的非线性二阶周期边值问题■解的存在性结果. 相似文献
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一类泛函方程的连续解 总被引:2,自引:0,他引:2
本文考虑泛函方程x(x(t))+f(x(t)-t)=0,在f满足一定单调性的条件下讨论了此方程连续解的性质、解的存在性和延拓性.其结果对于求解相应的泛函微分方程具有直接的应用. 相似文献
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该文讨论四阶常微分方程边值问题u(4)=f(t,u,u″),0≤t≤1,u(0)=u(1)=u″(0)=u″(1)=0解的存在性,其中f:[0,1]×R×R→R连续.文中提出了一个保证该问题解存在的两参数非共振条件,该条件是用椭圆描述的. 相似文献
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苟海德 《数学物理学报(A辑)》2020,(2):408-421
该文讨论了Banach空间中具有阻尼弹性系统L-拟mild解的存在性.这些结果改进和推广了一些相关的结论在常微分方程和偏微分方程方面.在非线性项满足单调条件和非紧性测度条件下,获得了该问题极大mild解的存在性.另外,给出例子说明该结果的可行性. 相似文献
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通过构造收敛的逼近列的方法给出了非李普希茨条件下无穷维随机微分方程dX=[AX+f(X)]dt+[BX+g(X)]dW的适度解的存在唯一性定理.文章推广了[1]和[2]的结论. 相似文献
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Existence and Approximate Controllability of Solutions for an Impulsive Evolution Equation with Nonlocal Conditions in Banach Space 下载免费PDF全文
Lixin Sheng Weimin Hu You-Hui Su Yongzhen Yun 《Journal of Nonlinear Modeling and Analysis》2024,6(1):194-209
In this article, we study the existence of mild solutions and approximate controllability for non-autonomous impulsive evolution equations with nonlocal conditions in Banach space. The existence of mild solutions and some conditions for approximate controllability of these non-autonomous impulsive evolution equations are given by using the Krasnoselskii''s fixed point theorem, the theory of evolution family and the resolvent operator. In particular,the impulsive functions are supposed to be continuous and the nonlocal item is divided into Lipschitz continuous and completely bounded. An example is given as an application of the results. 相似文献
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This paper is concerned with the existence for impulsive semilinear differential equations with nonlocal conditions. Using the techniques of approximate solutions and fixed point, existence results are obtained, for mild solutions, when the impulsive functions are only continuous and the nonlocal item is Lipschitz in the space of piecewise continuous functions, is not Lipschitz and not compact, is continuous in the space of Bochner integrable functions, respectively. 相似文献
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Nadjet Abada Ravi P. Agarwal Mouffak Benchohra Hadda Hammouche 《Applications of Mathematics》2011,56(2):227-250
In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some
densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed
point theorem for the sum of completely continuous and contraction operators. 相似文献
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In this paper, we study the solvability and optimal controls of a class of fractional integrodifferential evolution systems
with infinite delay in Banach spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence
and continuous dependence of mild solutions are investigated by utilizing the techniques of a priori estimation and extension
of step by steps. Finally, existence of optimal controls for system governed by fractional integrodifferential evolution systems
with infinite delay is proved. 相似文献
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R. Quintanilla 《Journal of Mathematical Analysis and Applications》2005,310(2):690-698
In this note we investigate a nonstandard problem determined by a system of differential equations and initial conditions. We use the techniques of the mild solutions to obtain continuous dependence estimates, uniqueness and existence of solutions. We also make some comments on nonexistence and nonuniqueness of solutions. 相似文献
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In this paper, we study the existence and uniqueness of mild solutions of neutral stochastic evolution equations with infinite delay and Poisson jumps in real separable Hilbert spaces. We study the continuous dependence of solutions on the initial value. The nonlinear term in our equations are not assumed to Lipschitz continuous. The results of this paper generalize and improve some known results. 相似文献
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Mohamed BOUAOUID 《应用数学学报(英文版)》2023,39(2):249-261
This paper deals with the existence, uniqueness and continuous dependence of mild solutions for a class of conformable fractional differential equations with nonlocal initial conditions. The results are obtained by means of the classical fixed point theorems combined with the theory of cosine family of linear operators. 相似文献
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Leszek Olszowy 《Central European Journal of Mathematics》2014,12(4):623-635
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system. 相似文献
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This work investigates the existence of globally Lipschitz continuous solutions to a class of Cauchy problem of quasilinear wave equations. Applying Lax's method and generalized Glimm's method, we construct the approximate solutions of the corresponding perturbed Riemann problem and establish the global existence for the derivatives of solutions. Then, the existence of global Lipschitz continuous solutions can be carried out by showing the weak convergence of residuals for the source term of equation. 相似文献
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Rajesh Dhayal Muslim Malik Syed Abbas Amar Debbouche 《Mathematical Methods in the Applied Sciences》2020,43(7):4107-4124
We study optimal control problems for a class of second-order stochastic differential equation driven by mixed-fractional Brownian motion with non-instantaneous impulses. By using stochastic analysis theory, strongly continuous cosine family, and a fixed point approach, we establish the existence of mild solutions for the stochastic system. Moreover, the optimal control results are derived without uniqueness of mild solutions of the stochastic system. Finally, the main results are validated with the aid of an example. 相似文献