Sentence examples for be an entire solution from inspiring English sources

Let f be an entire solution of Equation (1.4).

Let (w z) ) be an entire solution of (1.6) (or (1.7)), (S_{2}(r)) means the sum of characteristic functions of all coefficients in (1.6) (or (1.7)).

Let w = (w1, w2) be an entire solution of a type systems of algebraic differential equations of the form ( H ( w 2 ) ) m 1 = a ( z ) w 1 ( n ) w 1 ( n ) m 2 = p ( w 2 ), (1.5).

Suppose that f is an entire solution of (6) with (sigma(f)=sigma

Suppose f ( z ) is an entire solution of finite order satisfying λ ( f ) < δ ( f ), then we know δ ( f ) ≥ 1 by the conclusion of Corollary 1.3.

Example For a given positive integer k, f ( z ) = e z is an entire solution of the equation ( e z k − 2 + 1 ) f ( z + 2 ) − e z k − 1 f ( z + 1 ) − e 2 f ( z ) = 0.

If f ( z ) is an entire solution of (3.22), then σ p + 1 ( f ) ≥ σ 2. Proof Without loss of generality, we suppose that τ p ( A ) < τ p ( B ) < ∞.

end{cases} (4.28) Then, from [8], we know that (widetilde{v}(x)) is an entire solution to the Helmholtz equation (Delta{widetilde{v}}(x) + k_{1}^{2} {widetilde{v}}(x) = 0) in ({mathbb{R}}^{3}) satisfying the radiation condition (4.26), so it must vanish identically in ({mathbb {R}}^{3}).

In the same way as (i), we get λ ( 1 f ) = ∞, i.e., δ ( f ) = ∞, which contradicts the assumption that δ ( f ) < ∞.   (iii) Suppose f ( z ) is an entire solution of finite order satisfying λ ( f ) < δ ( f ), then we know δ ( f ) ≥ 1 by the conclusion of Corollary 1.3.

Consequently, ( u, v ) is a positive solution of (2.9); therefore, ( U, V ) is an entire positive solution of (1.1).

Suppose that is an entire subnormal solution of (2.6), where are polynomials in and with, and that and are linearly dependent.