Sentence examples for provide the existence from inspiring English sources

In Section 1, we provide the existence and nonexistence of solutions of system (1).

And then, we provide the existence, uniqueness, stability, and convergence for its CSM solutions.

We provide the existence of a positive solution for the quasilinear elliptic equation.

Hence, Theorem 1.1 cannot provide the existence of a coupled common fixed point of F and g.

Thus, Theorem 5.1 does not provide the existence of the common fixed point for the maps on this example.

These papers provide the existence of solutions, but do not provide information on the connectivity of the solution set.

Theorem 3.8 provides the existence of the solution u ∈ C ∞.

Consequently, Theorem 2.3 provides the existence and uniqueness of the fixed point of f. □.

Our main result provides the existence of a (positive) solution for problem (P).

Then the existence of a lower solution for (13) provides the existence of a unique solution of (13).

Then the existence of a lower solution for (3.1) provides the existence of a solution of (3.1).