Sentence examples for exactly one solution from inspiring English sources
This condition says that by Theorem 1 every initial value problem (1) and (2) with φ satisfying (3) has exactly one solution on the interval [ τ ( t 0 ), σ ] T, σ > t 0. It is also easy to show that this solution depends continuously on the initial function φ.
This condition says that, by Theorem 1, every initial problem (1) and (2) with φ satisfying (3) has exactly one solution on an interval [ α 0, σ ] T where σ > t 0. It is also easy to show that this solution depends continuously on the initial function φ.
Using the Lipschitz property of we can prove that the operator is contractive for each sufficiently small and from the Banach Fixed Point Theorem we conclude that there exists exactly one solution of problem (1.1), (1.2) on.
If (h(t)equivlambda_) on ([1,T]_{mathbf{Z}}), then problem (1.1) has exactly one solution.
(2) If (h(t)equivlambda_) on ([1,T]_{mathbf{Z}}), then problem (1.1) has exactly one solution.
(2) The line segment (OE_{k}) meets on the production possibility set (T_{k}) at the point (E_{k}), which is located on the production frontier, that is, there is exactly one solution of the inequalities of the production possibility set (T_{k}) and the line segment (OE_{k}).
(ii) Equation (1.1) has no positive solution for has exactly one positive solution for but and has exactly two positive solutions for (see Figure 1).
If f ( t, y ) is regressive and rd-continuous on T k, then equation (2) has exactly one global solution on T. Especially for the linear form of equation (2), we obtain simpler conditions in the following lemma.
(ii) Equation (3.19) has no positive solution for, and has exactly one positive solution for, and has exactly two positive solutions for.
(ii) Equation (1.1) has no positive solution for but has exactly one positive solution for and has exactly two positive solutions for.
