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

被引：3

作者：

Muravnik, Andrey B. ^{[1
]}

机构：

[1] RUDN Univ, Nikolskii Math Inst, Miklukho Maklaya ul 6, Moscow 117198, Russia

来源：

MATHEMATICS | 2024年 / 12卷 / 03期

关键词：

differential-difference operators; hyperbolic equations; nonlocal potentials; smooth solutions; CLASSICAL-SOLUTIONS;

D O I：

10.3390/math12030392

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：8