Sentence examples for multiple critical from inspiring English sources

This paper deals with the existence and multiplicity of symmetric solutions for a weighted semilinear elliptic system with multiple critical Hardy-Sobolev exponents and singular potentials in (mathbb{R}^{N}).

In order to obtain the multiplicity of nonnegative solutions for system (1.1), we need only to construct the multiple critical values of the corresponding energy functional.

This paper deals with the existence and multiplicity of symmetric solutions for a class of singular quasilinear elliptic systems involving multiple critical Hardy-Sobolev exponents in a bounded symmetric domain.

In this approach, invisible microbes play multiple critical roles.

Clinical outcome measures included hospital admission, in-hospital mortality, and multiple critical patient outcomes.

This is described below for a single critical bus; further work will consider multiple critical buses.

Most hospitals cannot provide an adequate response if multiple critical patients present simultaneously.

This bifurcation phenomena is called the bifurcation of multiple critical point.

Our data therefore reveal multiple critical functions for Erk5 in controlling ESC identity.

Integration of multiple critical software functions in a single embedded platform requires domain partitioning.

For system with multiple critical buses, we can use the average voltage error of multiple critical buses as the control reference and distribute it to the ESBCs either by the proposed consensus algorithm or by using a centralized optimization method.