Affiliation:
1. Nikol’skii Mathematical Institute, RUDN University, Miklukho–Maklaya ul. 6, 117198 Moscow, Russia
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.
Funder
Ministry of Science and Higher Education of the Russian Federation
Reference11 articles.
1. Nonclassical boundary-value problems. I;J. Math. Sci.,2008
2. Nonclassical boundary-value problems. II;J. Math. Sci.,2010
3. Mixed functional differential equations;Myshkis;J. Math. Sci.,2005
4. On some nonlinear elliptic differential functional equations;Hartman;Acta Math.,1966
5. Skubachevskiĭ, A.L. (1997). Elliptic Functional Differential Equations and Applications, Birkhäuser.
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献