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Initial value condition: (2.11).
(iii) Initial value condition: (2.11) .
with boundary value condition (k).
By boundary value condition, we have (2.12).
The boundary value condition holds (3.35).
Thus the boundary value condition holds, then.
This paper deals with the existence of solutions of (1 - 3) with periodic-like boundary value condition, Neumann boundary value condition, or Dirichlet boundary value condition, respectively.
The boundary value condition (1.4) implies that (2.25).
which together with the boundary value condition (1.4) implies (2.8).
Thus we call (4) the periodic-like boundary value condition.
From the boundary value condition, we deduce that (2.10).
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