On an integro-differential equation with almost difference kernel on the half-line |
| |
Authors: | Kh A Khachatryan E A Khachatryan |
| |
Institution: | 1. Institute of Mathematics, National Academy of Sciences of Armenia, Yereven, Armenia 2. Erevan State University, Erevan, Armenia
|
| |
Abstract: | We study the solvability of a class of integro-differential equations with almost difference kernel on the positive half-line. Using a special three-factor decomposition of the original integro-differential operator, we obtain sufficient conditions for the solvability of this equation in the class of tempered absolutely continuous functions. Under additional conditions on the kernel of the corresponding homogeneous equation with some value of the parameter occurring in it, we prove the existence of a nontrivial absolutely continuous solution, which, depending on the sign of the first moment of the kernel, is either a bounded function or has the asymptotics O(x), x → ∞. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|