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
收藏
页数：8
相关论文
共 11 条
[1]  
Gelfand I. M., 1953, Uspekhi Matem. Nauk., V8, P3
[2]   ON SOME NON-LINEAR ELLIPTIC DIFFERENTIAL-FUNCTIONAL EQUATIONS [J].
HARTMAN, P ;
STAMPACCHIA, G .
ACTA MATHEMATICA UPPSALA, 1966, 115 (3-4) :271-+
[3]  
MYSHkIS A. D., 2005, J. Math. Sci., V129, P4111, DOI [10.1007/s10958-005-0345-2, DOI 10.1007/S10958-005-0345-2]
[4]   Boundary-value problems for elliptic functional-differential equations and their applications [J].
Skubachevskii, A. L. .
RUSSIAN MATHEMATICAL SURVEYS, 2016, 71 (05) :801-906
[5]  
Skubachevskii A. L., 1997, Oper. Theory Adv. Appl, V91
[6]  
Skubachevskii A.L., 2008, J MATH SCI-U TOKYO, V155, P199, DOI [10.1007/s10958-008-9218-9, DOI 10.1007/S10958-008-9218-9]
[7]  
Skubachevskii A.L., 2010, J MATH SCI-U TOKYO, V166, P377, DOI [10.1007/s10958-010-9873-5, DOI 10.1007/S10958-010-9873-5]
[8]   Smooth Solutions of Hyperbolic Equations with Translation by an Arbitrary Vector in the Free Term [J].
Zaitseva, N. V. ;
Muravnik, A. B. .
DIFFERENTIAL EQUATIONS, 2023, 59 (03) :371-376
[9]   Classical Solutions of a Multidimensional Hyperbolic Differential-Difference Equation with Shifts of Various Directions in the Potentials [J].
Zaitseva, N. V. .
MATHEMATICAL NOTES, 2022, 112 (5-6) :872-880
[10]   HYPERBOLIC DIFFERENTIAL-DIFFERENCE EQUATIONS WITH NONLOCAL POTENTIALS [J].
Zaitseva, N., V .
UFA MATHEMATICAL JOURNAL, 2021, 13 (03) :36-43
12