Sentence examples for method some new from inspiring English sources

Combining with the Halanay inequality and the Lyapunov functional method, some new sufficient conditions are derived for the model to be globally exponentially stable.

The theoretical development is composed of full-mode-participation method, some new findings in flutter mechanism and stabilization and computational fluid dynamics (CFD) techniques and application, and some probabilistic assessment approaches are proposed and applied in wind-induced vibration including flutter instability, buffeting response and vortex-induced vibration.

Based on Lyapunov second method, some new absolute stability conditions were proposed.

Then, by using the variational method, some new existence results are obtained.

Different from the free-weighting matrix method, some new sharper summation inequalities are developed via auxiliary functions.

By the properties of Green's function, the Guo-Krasnosel'skii fixed-point theorem, the Leggett-Williams fixed-point theorem, and the upper and lower solutions method, some new results on the existence of positive solutions are obtained.

To enable these methods, some new types of designs are defined.

Based on variational methods, some new results are obtained in regard to the existence of solutions.

Under suitable hypotheses and by using variational methods, some new criteria to guarantee that the fractional differential system has at least two nontrivial and nonnegative solutions are obtained.

Under some natural assumptions, by employing variational methods, some new results for the existence of at least two nontrivial and nonnegative solutions of the system ((P_{lambda })) are obtained.

Based on the fact that the (PS) condition can be replaced by the weaker Cerami condition for some deformation theorems which are the footstone for minimax methods, some new p-superlinear growth conditions were established in order to weaken ((AR)).