具有非局部条件的二阶发展方程解的存在性
Existence of Solutions for Second Order Evolution Equations with Nonlocal Conditions
DOI: 10.12677/aam.2025.1412492, PDF,    科研立项经费支持
作者: 马田甜, 史 伟：新疆农业大学数理学院，新疆 乌鲁木齐
关键词: 发展方程；非紧性测度；温和解；Evolution Equations； Noncompact Measure； Mild Solution
摘要: 本文讨论一类具有非局部条件的二阶发展方程温和解的存在性和唯一性。基于余弦函数理论、不动点定理与非紧性测度方法，证明了在紧半群或非紧半群情形下温和解的存在性和唯一性。此外，我们还给出了一个具体的应用实例来阐释我们的结果。
Abstract: This paper deals with the existence and uniqueness of mild solutions for a class of second order evolution equations problem with non-local conditions. This discussion is based on the cosine function theory, the fixed point theorem and the noncompact measure method. We prove the existence and uniqueness of mild solutions when the associated semigroup is compact or not. In addition, an example is presented to illustrate our theoretical results.
文章引用：马田甜, 史伟. 具有非局部条件的二阶发展方程解的存在性[J]. 应用数学进展, 2025, 14(12): 125-135. https://doi.org/10.12677/aam.2025.1412492

参考文献

[1] Byszewski, L. (1991) Theorems about the Existence and Uniqueness of Solutions of a Semilinear Evolution Nonlocal Cauchy Problem. Journal of Mathematical Analysis and Applications, 162, 494-505. [Google Scholar] [CrossRef] 
[2] Byszewski, L. and Lakshmikantham, V. (1991) Theorem about the Existence and Uniqueness of a Solution of a Nonlocal Abstract Cauchy Problem in a Banach Space. Applicable Analysis, 40, 11-19. [Google Scholar] [CrossRef] 
[3] Byszewski, L. and Akca, H. (1997) On a Mild Solution of a Semilinear Functional‐Differential Evolution Nonlocal Problem. International Journal of Stochastic Analysis, 10, 265-271. [Google Scholar] [CrossRef] 
[4] Byszewski, L. and Akca, H. (1998) Existence of Solutions of a Semilinear Functional-Differential Evolution Nonlocal Problem. Nonlinear Analysis: Theory, Methods & Applications, 34, 65-72. [Google Scholar] [CrossRef] 
[5] Byszewski, L. (1998) Application of Properties of the Right-Hand Sides of Evolution Equations to an Investigation of Nonlocal Evolution Problems. Nonlinear Analysis: Theory, Methods & Applications, 33, 413-426. [Google Scholar] [CrossRef] 
[6] Krasnoselskii, M. (1964) Topological Methods in the Theory of Nonlinear Integral Equations. Pergamon.
[7] Travis, C.C. and Webb, G.F. (1978) Cosine Families and Abstract Nonlinear Second Order Differential Equations. Acta Mathematica Academiae Scientiarum Hungaricae, 32, 75-96. [Google Scholar] [CrossRef] 
[8] Travis, C. and Webb, G. (1997) Compactness, Regularity, and Uniform Continuity Properties of Strongly Continuous Cosine Families. Houston Journal of Mathematics, 3, 555-567.
[9] Banaś, J. and Goebel, K. (1980) Measure of Noncompactness in Banach Space. Marcel Dekker Inc.
[10] Heinz, H. (1983) On the Behaviour of Measures of Noncompactness with Respect to Differentiation and Integration of Vector-Valued Functions. Nonlinear Analysis: Theory, Methods & Applications, 7, 1351-1371. [Google Scholar] [CrossRef] 
[11] Mönch, H. (1980) Boundary Value Problems for Nonlinear Ordinary Differential Equations of Second Order in Banach Spaces. Nonlinear Analysis: Theory, Methods & Applications, 4, 985-999. [Google Scholar] [CrossRef] 
[12] Hilfer, R. (2000) Applications of Fractional Calculus in Physics. World Scientific.
[13] Fattorini, H. (1986) Second Order Linear Differential Equations in Banach Space. North-Holland, 108.

为你推荐