Sentence examples for provides the existence from inspiring English sources

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

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

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

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).

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

The results of the analysis provide the existence and stability of the non-linear impacting periodic motions of the pendulum, based on various system parameters.

Fourier-transform infrared spectroscopic and X-ray photoelectron spectroscopic studies provided the existence of interactions in the PMVT blends and complexes.

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

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.