The solvability of a boundary-value periodic problem

Authors

  • Ya. B. Petrovskii
  • G. P. Khoma

Abstract

In the space of functions B a 3+ ={g(x, t)=−g(−x, t)=g(x+2π, t)=−g(x, t+T3/2)=g(x, −t)}, we establish that if the condition aT 3 (2s−1)=4πk, (4πk, a (2s−1))=1, k ∈ ℤ, s ∈ ℕ, is satisfied, then the linear problem u u −a 2 u xx =g(x, t), u(0, t)=u(π, t)=0, u(x, t+T 3 )=u(x, t), ℝ2, is always consistent. To prove this statement, we construct an exact solution in the form of an integral operator.

Published

25.02.1997

Issue

Section

Research articles

How to Cite

Petrovskii, Ya. B., and G. P. Khoma. “The Solvability of a Boundary-Value Periodic Problem”. Ukrains’kyi Matematychnyi Zhurnal, vol. 49, no. 2, Feb. 1997, pp. 302–308, https://umj.imath.kiev.ua/index.php/umj/article/view/5006.