Sentence examples for be a decreasing solution from inspiring English sources

Indeed, let (v_{epsilon}(x)) be a decreasing solution of (1.1).

If (v(x)) is an increasing solution to (1.1), then (v L-x)) is a decreasing solution.

Let be a monotone decreasing solution of (1.1) satisfying conditions (1.4) and (1.5).

Thus {y n } is a positive decreasing solution of inequality (2.4), a contradiction.

Case 2: Assume that Δz n < 0. Clearly Δy n < 0. Then as in case 2 of Theorem 2.4, we find that {y n } is a positive decreasing solution of inequality (2.20).

It is also observed that the first solution is a decreasing function of λ, whereas the second solution is an increasing function of λ.

(i) {s k } is an increasing sequence of lower solutions to (1.1 - 1.2 1.1 - 1.2i) {S k } is a decreasing sequence on upper solutI.ns to (1.1)-(1.2) on ii (iii) s k ≤ S k, for k ≥ 1. Proof.

The sequence ((underline{w}^{(n)},underline{z}^{(n)})), (ngeq1), is an increasing sequence of lower solutions of BVP (1); the sequence ((overline{w}_{n},overline{z}_{n})), (ngeq1) is a decreasing sequence of upper solutions of BVP (1).

(25) Then we have (i) The sequence ((underline{w}^{(n)},underline{z}^{(n)})), (ngeq1), is an increasing sequence of lower solutions of BVP (1);   (ii) the sequence ((overline{w}_{n},overline{z}_{n})), (ngeq1) is a decreasing sequence of upper solutions of BVP (1).

We can clearly see that the difference between the optimal solution (MDP) and the approximated solution (LP) is a decreasing function of the budget size.

Let be a positive, monotone decreasing solution of (2.1).