On Global Solutions of Hyperbolic Equations with Positive Coefficients at Nonlocal Potentials

Andrey B. Muravnik ()
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Andrey B. Muravnik: Nikol’skii Mathematical Institute, RUDN University, Miklukho–Maklaya ul. 6, 117198 Moscow, Russia

Mathematics, 2024, vol. 12, issue 3, 1-8

Abstract: We study hyperbolic equations with positive coefficients at potentials undergoing translations with respect to the spatial independent variable. The qualitative novelty of the investigation is that the real part of the symbol of the differential-difference operator contained in the equation is allowed to change its sign. Earlier, only the case where the said sign is constant was investigated. We find a condition relating the coefficient at the nonlocal term of the investigated equation and the length of the translation, guaranteeing the global solvability of the investigated equation. Under this condition, we explicitly construct a three-parametric family of smooth global solutions of the investigated equation.

Keywords: differential-difference operators; hyperbolic equations; nonlocal potentials; smooth solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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