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Existence of solutions of the wave equation involving the distributional Henstock-Kurzweil integral. (English) Zbl 1249.35222

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.

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
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