Sentence examples for solution which lies from inspiring English sources

Thus, (4) has the periodic solution which lies in Γ.

Then Theorem 1.1 implies that model (4) has a 2π-periodic solution which lies in ((0,1)), see Figure 1. Figure 1 Simulations of (S t)) and (I t)) of Example 1.

Consequently, according to the principle of Schauder [16], operator (Z_{f}) has a fixed point in the ball (E 0,A) {subset W}_{2}^{1}(mathbb{R})). Therefore the equation Ly equiv{- y}"' + q ( x,y )y + lambda y = fmathbf {in}L_{2}(mathbb{R}) has a solution y which lies in a ball of radius A in (W_{2}^{1}(mathbb{R})).

Hence, the true solution υ, which lies in between, must converge uniformly to w and the proof of (ii) is completed.

Thus, it must be the case that the maximum of f is constrained to solutions for which lies in the interval.

(ii) If, then (1.11) does not have oscillatory solution with or.   (iii) If, then, except possibly for the first semicycle, every oscillatory solution of (1.11) which lies in the invariant interval has semicycles that are either of length at least or of length at most.  .

If, then, except possibly for the first semicycle, every oscillatory solution of (1.11) which lies in the invariant interval has semicycles of length at most.

(i) If, then, except possibly for the first semicycle, every oscillatory solution of (1.11) which lies in the invariant interval has semicycles of length at most.

If, then, except possibly for the first semicycle, every oscillatory solution of (1.11) which lies in the invariant interval has semicycles that are either of length at least or of length at most.

Thus is a solution of -Laplacian BVP (1.1 - 1.2) which lies between and.

Nanocrystal colloids offer the primary advantage of organic materials which lies in solution processability.