Differential and Integral Equations

Existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral

Wei Liu, Yueping Lu, Ying Wang, and Guoju Ye

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Abstract

In this paper we study the application of a general integral called a distributional Henstock-Kurzweil integral which includes the Henstock-Kurzweil integral and the wide Denjoy integral. We prove the existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral by using Schauder's fixed-point theorem.

Article information

Source
Differential Integral Equations, Volume 24, Number 11/12 (2011), 1063-1071.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012876

Mathematical Reviews number (MathSciNet)
MR2866011

Zentralblatt MATH identifier
1249.35222

Subjects
Primary: 35L05: Wave equation 26A39: Denjoy and Perron integrals, other special integrals 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 46B40: Ordered normed spaces [See also 46A40, 46B42] 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22] 46G12: Measures and integration on abstract linear spaces [See also 28C20, 46T12]

Citation

Lu, Yueping; Ye, Guoju; Liu, Wei; Wang, Ying. Existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral. Differential Integral Equations 24 (2011), no. 11/12, 1063--1071. https://projecteuclid.org/euclid.die/1356012876


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