Sentence examples for a strict solution of from inspiring English sources

Then (omega_in W_) is a strict solution of the inverse problem (1.5 - 1.6 1.5 - 1.6nly if (vandhi(x, y,t;onlya_) equif0), a.e. on (Omega_{T}).

In order to obtain the existence of at least three solutions of (1.1), we introduce the notion of a strict solution-tube of (1.1).

In order to establish our multiplicity result, we introduce the notion of a strict solution-tube of (1.1) which will permit one to obtain solutions satisfying (|x t -v(t)|x t -v)) for all (t in[0,1]).

We say that ((v,r)) is a strict solution-tube of ( 1.1 ) if the following conditions hold: (i) there exists a l.s.c.

The fact that ((v_{j},r_{j})) is a strict solution-tube of (1.1), when (j in{1,2}), permits us to get more precision on the localization of the solutions of (3.1 j ).

Observe that the periodic boundary condition and the fact that ((v_{j},r_{j})) is a strict solution-tube of (1.1) imply that begin{aligned} bigl| x(a -v_{j}(a -v_{j &lebigl| x(b)-v_{j}(b)bigr| - r_{j}(b) + bigl| v_{j}(b)-v_{j}(a bigr| + r_{j}(b) &lebigl|(a) - delta_{j}.

To this aim, we introduce the notion of a strict solution-tube.

Obviously, a strict solution-tube is a solution-tube of (1.1).

We recall that a strict lower solution of (1.2) is a lower solution which is not a solution of (1.2).

Then the solution x ¯ of (3.1) is a strict sup solution of (1.1) for ε > 0 small enough.

Now we prove that the solution x ¯ of (3.1) is a strict sup solution of (1.1) for ε > 0 small enough.