Sentence examples for have an upper solution from inspiring English sources

We have an upper solution independent of M, for all M large enough.

end{aligned} (3.15) However, this problem has an upper solution (U_{t}).

then (2.14) has an upper solution β such that u 2 ≤ β < u 2 + a ( N − 2 ).

Thus, by Proposition 2.1, problem (3.4) has an upper solution β such that tilde{A}_{1}leqbetaleqtilde{B}_{1}.

The conclusion is that these isotopic mixtures are incompatible at ambient temperatures and have an upper critical solution temperature.

Then we have established an upper solution v ¯ ( r, t ) = ω ( r ; μ ¯ ( t ) ) to the problem (3), which converges to the steady state, i.e. v ¯ ( r, t ) → ω ( r ; μ ∗ ) = ω ( r ), as  t → ∞.

The modified double-lattice model successfully describes the phase behaviours of binary polymer solutions having an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST).

The model successfully describes the liquid liquid equilibria having an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST), but cannot predict the closed miscibility loop phase behavior.

The blend system had an upper critical solution temperature (UCST) type phase diagram.

The predicted phase diagram has an upper critical solution temperature (UCST) with a critical point of 114 °C.

Therefore, for every so large, we have a lower and an upper solution to, respectively, such that (2.2) is satisfied and so, Corollary 2.5 guarantees that problem has at least one solution in the sense of distributions.