Sentence examples for upper solution of the from inspiring English sources

We now choose an upper solution of the form (3.21).

Similarly, (bar{v}) is a strict upper solution of the problem (3.8).

We see that is an upper solution of the equation (3.20).

Therefore, we have proved that is a global upper solution of the system (1.1).

Similarly, is an upper solution of the BVP (1.1) if (2.7).

Now, let ((alpha, beta)) be a coupled normal lower and normal upper solution of the integral equation of (34).

Let and be, respectively, lower and upper solutions of the boundary value problem (1.1).

Assume that, are lower and upper solutions of the BVP (1.1) such that.

(comparison result) Assume that, are lower and upper solutions of the boundary value problem (1.1).

(u_{0}) and (v_{0}) are coupled lower and upper solutions of the equation (Lu=Nu).

Assume that Φ and Ψ are lower and upper solutions of the problem (2) such that Φ ≤ Ψ.