By virtue of Mönch's fixed-point theorem and the technique of measure of weak noncompactness and got some conditions of positive solutions.
Hopefully we'll get some good conditions in the morning.
In Section 3, we mainly use the Riccati transformation technique to get some sufficient conditions which guarantee that every solution of (1.1) is oscillatory or the limit inferior converges to zero.
Since the regularity of weak solutions to the 3D Navier-Stokes equations is hard to get, some related conditions or criteria for the regularity of the weak solutions are considered, such as the well-known Serrin type criterion [7] and the Beale-Kato-Majda type criterion [8].
"Hopefully, we'll get some good conditions in the morning, and those other guys have to play 36 holes in a row at a U.S. Open, which isn't easy," said defending Jordan Spieth.
I have been really lucky in my life, health-wise; if/when I get some chronic condition, I had better medicate heavily so that I don't get divorced/disowned by children.
Lastly, due to the nonsingularity of the matrix being closely related to the lower bound for the rank of the matrix, using the results in Section 2, we can get some new sufficient conditions for nonsingular matrices, such as the theorems and corollaries in Section 3.
Especially, we have got some sufficient conditions for the global stability of the endemic equilibrium.
