Sentence examples for solution emanating from inspiring English sources

According to [19], when (gammage1), the solution emanating from the initial data will resolve itself into one or more solitary waves, sometimes accompanied by additional structure.

Conditions to ensure the existence of several branches of T-periodic solution emanating from x 0 are provided by means of suitably defined Malkin bifurcation functions.

However, a solution emanating from our experimental study consists of firstly splitting the graph under (N_{node}) (times ) (N^{map}_{core}) subgraphs in the input stage.

Similarly, we give the following definition: if x n is a solution of a discrete system, x n will be called a homoclinic solution emanating from 0 if x n → 0 as |n| → +∞.

Recent work on HS demonstrated its inherent bent shape and flexibility in solution emanating primarily from the N-acetylated and less highly sulfated regions of the GAG polymer [ 27].

We first take a as a bifurcation parameter and give the bifurcation solutions emanating from the semi-trivial solution ( 0, θ c ). Theorem 3.3 Assume c > λ 1.

We show the following: There are unbounded continuums consisting of non-radially symmetric solutions emanating from the second and third eigenvalues.

Next, we investigate the periodic solutions emanating from the Hopf bifurcations H 1, H 2 and H 3. The branch of unstable periodic solutions that emerges from H 1 consists of symmetric solutions.

In Section 3, by investigating the bifurcation of positive solutions emanating from the semi-trivial solution ( θ a, 0 ; c ), we give a sufficient and necessary condition for the existence of positive solutions to (1.1) and establish the multiplicity result of positive solutions when γ is suitably large.

Although there exist some gaps in the proofs of Rabinowitz's Theorems 1.27, 1.40, and 1.27 has been used several times in the literature to analyze the global behavior of the component of nodal solutions emanating from u = 0 in wide classes of boundary value problems for equations and systems [1, 2, 8, 9].

By Lemmas 3.3, 3.4, and 3.5, for any j ∈ ℕ, there exists an unbounded connected component C j of the set of nontrivial solutions emanating from (0, λ j (p)) such that ( u, λ ) ∈ C j implies u has exactly j - 1 simple zeros in (0,1).