Entire solutions of one linear implicit differential-difference equation in Banach spaces

  • S. L. Gefter
  • A. L. Piven’


We establish the existence and uniqueness conditions for the solution for the initial problem $Bu\prime (z) = Au(z + h) + f(z),\; z \in C, u(0) = u_0$ in the classes of entire functions of exponential type. Closed linear operators $A$ and $B$ act on Banach spaces and can be degenerate. We also present an example of application of abstract results to partial differential equations.
How to Cite
Gefter, S. L., and A. L. Piven’. “Entire Solutions of One Linear Implicit Differential-Difference Equation in Banach Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 8, Aug. 2018, pp. 1044-57, https://umj.imath.kiev.ua/index.php/umj/article/view/1616.
Research articles