Sobolev型分数阶随机发展方程非局部问题 Mild解的存在性
Existence of Mild Solutions for Nonlocal Problems of Fractional Stochastic Evolution Equations of Sobolev Type
摘要: 本文利用不动点定理和预解算子理论讨论了 Hilbert 空间中 Sobolev 型α∈(1,2)阶 Riemann-Liouville 分数阶随机发展方程非局部问题 mild 解的存在性。
Abstract: In this paper, by utilizing the resolvent operator theory and the fixed point theorem, the existence of mild solutions for nonlocal problems of Riemann-Liouville fractional stochastic evolution equations of Sobolev-type with order α∈(1,2) is discussed in Hilbert spaces.
文章引用：白玉洁. Sobolev型分数阶随机发展方程非局部问题 Mild解的存在性[J]. 理论数学, 2022, 12(1): 132-147. https://doi.org/10.12677/PM.2022.121018

参考文献

[1] Ponce, R. (2016) Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness. Abstract and Applied Analysis, 2016, Article ID: 4567092. [Google Scholar] [CrossRef] 
[2] Brill, H. (1977) A Semilinear Sobolev Evolution Equation in Banach Space. Journal of Differ- ential Equations, 24, 412-425. [Google Scholar] [CrossRef] 
[3] Showalter, R.E. (1972) Existence and Representation Theorems for a Semilinear Sobolev E- quation in Banach Space. SIAM Journal on Mathematical Analysis, 3, 527-543. [Google Scholar] [CrossRef] 
[4] Mahmudov, N.I. (2014) Existence and Approximate Controllability of Sobolev Type Frac- tional Stochastic Evolution Equations. Bulletin of the Polish Academy of Sciences: Technical Sciences, 62, 205-215. [Google Scholar] [CrossRef] 
[5] Benchaabane, A. and Sakthivel, R. (2017) Sobolev-Type Fractional Stochastic Differential E- quations with Non-Lipschitz Coefficients. Journal of Computational and Applied Mathematics, 312, 65-73. [Google Scholar] [CrossRef] 
[6] Yang, H. (2020) Existence Results of Mild Solutions for the Fractional Stochastic Evolution Equations of Sobolev Type. Symmetry, 12, Article 1031. [Google Scholar] [CrossRef] 
[7] Ahmed, H.M. (2017) Sobolev-Type Fractional Stochastic Integrodifferential Equations with Nonlocal Conditions in Hilbert Space. Journal of Theoretical Probability, 30, 771-783.[CrossRef] 
[8] Chang, Y.K., Pereira, A. and Ponce, R. (2017) Approximate Controllability for Fractional Dif- ferential Equations of Sobolev Type via Properties on Resolvent Operators. Fractional Calculus and Applied Analysis, 20, 963-987. [Google Scholar] [CrossRef] 
[9] Pazy, A. (1983) Semigroups of Linear Operators and Applications to Partial Differential E- quations. Springer-Verlag, New York.
[10] Chang, Y.K., Pei, Y.T. and Ponce, R. (2019) Existence and Optimal Controls for Fractional Stochastic Evolution Equations of Sobolev Type via Fractional Resolvent Operators. Journal of Optimization Theory and Applications, 90, 558-572. [Google Scholar] [CrossRef] 
[11] Kamenskii, M., Obukhovskii, V. and Zecca, P. (2001) Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. De Gruyter, Berlin. [Google Scholar] [CrossRef] 
[12] 郭大钧, 孙经先. 抽象空间常微分方程[M]. 第2版. 济南: 山东科学技术出版社, 2005.
[13] Ichikawa, A. (1982) Stability of Semilinear Stochastic Evolution Equations. Journal of Mathe- matical Analysis and Applications, 90, 12-44. [Google Scholar] [CrossRef] 
[14] Yang, H. and Zhao, Y.J. (2020) Controllability of Fractional Evolution Systems of Sobolev Type via Resolvent Operators. Boundary Value Problem, 2020, Article No. 119. [Google Scholar] [CrossRef] 

为你推荐