## Advances in Operator Theory

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

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

Fuli Wang, Hua Zhou, and Shiyou Weng

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#### Abstract

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

**Source**

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

**Dates**

Received: 22 July 2018

Accepted: 13 November 2018

First available in Project Euclid: 1 December 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.aot/1543633241

**Digital Object Identifier**

doi:10.15352/aot.1807-1400

**Mathematical Reviews number (MathSciNet)**

MR3883150

**Zentralblatt MATH identifier**

07009323

**Subjects**

Primary: 45G15: Systems of nonlinear integral equations

Secondary: 45M99 46A04

**Keywords**

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

#### Citation

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. https://projecteuclid.org/euclid.aot/1543633241

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