Sentence examples for solutions is established from inspiring English sources

Then, the existence of weak solutions is established.

Moreover the polynomial decay rate for solutions is established.

The uniqueness of global weak solutions is established with certain assumptions.

The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones.

A weak convergence theorem for common solutions is established in a uniformly smooth and uniformly convex Banach space.

The existence result of positive solutions is established by using the fixed point index theory of cone mapping.

The existence of mild solutions are established.

New criterions, ensuring the existence of mild solutions, are established.

The existence and expression of random periodic solutions are established.

Two logarithmically blow-up criteria of smooth solutions are established.

The conditions for the existence of positive solutions are established.