一类非线性积-微分方程极值解的存在性定理
Existence Theorems of Extremal Solutions for a Class of Nonlinear lntegro-Differential Equations
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Abstract: In this paper, the following initial value problem for nonlinear integro-differential equationis is considered, where Using the method of upper and lower solutions and the monotone iterative technique.We obtain existence results of minimal and maximal solutions.
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[1] 孙经先、刘立山,Banach空间中混合型微分-积分方程的单调迭代法,系统科学与数学,13(2)(1993), 160-166. [2] Sun Jingxian and Zhao Zengqin, Extremal solutions of initial Value problem for integro-differential equations of mixed type in Banach Spaces, Ann. of Diff: Eqs., 8, 4(1992),469-475. [3] S. K. Kaul and A. S. Vatsala, Monotone method for intearo-differential equation with periodic boundary conditions, Applicable Analysis, 21(1986), 297-305. [4] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities Acad. Press (1969). [5] R. Kress, Linear Integral Equations, Springer-Verlag, Berlin Heidelberg(1989).
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