EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY

Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (12): 1103-1114.

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EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY

丁协平

Sichuan Normal University, Chengdu

收稿日期:1986-07-26 出版日期:1987-12-18 发布日期:1987-12-18
基金资助:
the Science Fund of the Chinese Academy of Sciences

EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY

Ding Xie-ping

Sichuan Normal University, Chengdu

Received:1986-07-26 Online:1987-12-18 Published:1987-12-18

摘要/Abstract

摘要： In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12].

关键词: generalized Oseen equation, local projection stabilization, Crouzeix-Raviart element

Abstract: In this paper, we prove several existence theorems of random solutions to nonlinear random Volterra integral equations under the weak topology of Banach spaces. Then, as applications, we obtain the existence theorems of weak random solutions to random differential equations. Existence of extremal random solutions and a random comparison theorem for these random equations are also obtained. Our theorems improve and extend the corresponding results in [4,5,10,11,12].

Key words: generalized Oseen equation, local projection stabilization, Crouzeix-Raviart element

丁协平. EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(12): 1103-1114.

Ding Xie-ping . EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(12): 1103-1114.

参考文献

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EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY

EXISTENCE AND COMPARISON RESULTS OF SOLUTIONS FOR NONLINEAR RANDOM INTEGRAL AND DIFFERENTIAL EQUATIONS RELATIVE TO WEAK TOPOLOGY

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