Sentence examples for without uniqueness from inspiring English sources

Nonlinear boundary value problems may have solutions without uniqueness.

In fact, one also can show the global existence of weak solutions without uniqueness if the compatibility conditions (1.9), (1.10) are not valid.

To show that the boundary value problem (10), (13 - 16 13 - 16olutions may be withave uniquenesolutionscall the following well-known theoremay

Although the existence of attractors has been derived for many classes of partial differential equations without uniqueness, to the best of our knowledge, little seems to be known for singular/degenerate equations, expecially in the quasilinear case.

Thanks to these theories, several results concerning attractors in the case of equations without uniqueness have been obtained recently for differential inclusion [5, 6], parabolic equations [8 10], the phase-field equation [11], the wave equation [12], the three-dimensional Navier-Stokes equation [3, 13], etc.

Without uniqueness, companies have a lot more competition and fewer tools to beat competitors.

It sees British Sea Power attempting the most awkward trick in rock: broadening appeal beyond cult-dom without sacrificing uniqueness.

Rus [3] proved that the conclusions of Theorem 1.1 hold without the uniqueness assertion but under a slightly weaker contractive assumption; for other results in this direction, we refer to Subrahmanyam [4], Kasahara [5] and Hicks and Rhoades [6].

By making these small changes as a collective, we can bring a new level of sustainability to every travel experience, ensuring that although the world is flat, it's not without luster, uniqueness, and above all, loved.

"Ellison grants blacks their uniqueness without separating us from the larger culture," Shelby Steele, the author of "The Content of Our Character," said.

It appears to be the philosopher's stone or holy grail of contemporary urban intervention, which is to do something as phenomenally successful as New York's High Line, one of whose virtues is uniqueness, without looking too much like the High Line.