Sentence examples for solutions are established from inspiring English sources

Some existence results of sign-changing solutions are established.

Firstly, four SUS solutions are established to satisfy demands and detailed descriptions are introduced.

Limiting cases are examined and fair agreements with well-known solutions are established.

Variational formulations for the TM and TE polarizations are derived and existence and uniqueness of weak solutions are established.

Two different semi-analytical solutions are established, by using the in-vacuum linear mode shapes of the beam and Hermitian finite element basis functions.

Numerical solutions are established to show a wide range of dispersion behaviour which is delicately dependent on the material parameters and pre-stress in each layer.

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.