Advances in Operator Theory

Existence of weak solutions for an infinite system of second order differential equations

Fuli Wang, Hua Zhou, and Shiyou Weng

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‎ ‎In this paper‎, ‎we investigate the existence of weak solutions for a boundary value problem of an infinite system of second order differential equations‎. ‎As the main tool‎, ‎a new Krasnosel'skii type fixed point theorem in Fréchet spaces is established in conjunction with the technique of measures of weak noncompactness‎.

Article information

Adv. Oper. Theory, Volume 4, Number 2 (2019), 514-528.

Received: 22 July 2018
Accepted: 13 November 2018
First available in Project Euclid: 1 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 45G15: Systems of nonlinear integral equations
Secondary: 45M99‎ ‎46A04

Fréchet space‎ ‎infinite system of differential equation ‎ ‎‎measures of weak noncompactness‎ ‎ ‎fixed point


Wang, Fuli; Zhou, Hua; Weng, Shiyou. Existence of weak solutions for an infinite system of second order differential equations. Adv. Oper. Theory 4 (2019), no. 2, 514--528. doi:10.15352/aot.1807-1400.

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