Lu, Yueping; Ye, Guoju; Liu, Wei; Wang, Ying Existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral. (English) Zbl 1249.35222 Differ. Integral Equ. 24, No. 11-12, 1063-1071 (2011). Summary: 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. Cited in 1 Document MSC: 35L71 Second-order semilinear hyperbolic equations 35L05 Wave equation 26A39 Denjoy and Perron integrals, other special integrals 28B05 Vector-valued set functions, measures and integrals 46G12 Measures and integration on abstract linear spaces Keywords:distributional Henstock-Kurzweil integral; Denjoy integral; wave equation PDF BibTeX XML Cite \textit{Y. Lu} et al., Differ. Integral Equ. 24, No. 11--12, 1063--1071 (2011; Zbl 1249.35222)