Sentence examples for is defined later from inspiring English sources

For the quintic nonlinearities term (mathcal{G}), which is defined later in (25), we assume the following.

(G x,y)=G(M x,y)) is the Green function which is defined later in Theorem  3.1.

For this purpose, let us define the functional J : = ∫ − s s | ϕ ( M ) | 2 d x ∫ − s s r ˜ | ϕ | 2 d x ( ϕ ∈ W ( M, 2 ), ϕ ≢ 0 ), where is defined later.

and the boundary condition u ( 0, t ) = u ( π, t ) = 0. To consider a more general case, we will replace D in (2) by a given function a ( t ) which is defined later.

While (H 3) is a technical condition ensuring that D 0, γ 1, p is embedded compactly into L2, where D 0, γ 1, p is the natural energy space related to problem (1.1), which is defined later in this section.

The deal allows Syrian government warplanes to continue to fly missions in some areas that are to be defined later.

where will be defined later.

for positive constants and will be defined later.

where,,, and are real constants, (here, and will be defined later), and are positive real numbers.

where (w_{1}), α, and (C_{7}) are positive constants which will be defined later.

P is a phase space that will be defined later (see Definition 2.1).