Sentence examples for methods in critical from inspiring English sources

Our approach is based on the well-known mountain pass theorem and minimax methods in critical point.

via different methods in critical point theory such as Morse theory [6], index theory [9] and minimax methods [7].

Some existence and multiplicity of periodic solutions are obtained for nonautonomous second order Hamiltonian systems with sublinear nonlinearity by using the least action principle and minimax methods in critical point theory.

In this paper, some new existence theorems are obtained for multiple periodic solutions of second order Josephson-type differential systems with partially periodic potential by using the minimax methods in critical point theory, which generalize and improve some known results in the literature.

Objective: To identify the exclusion criteria for the major severity of disease scoring methods in critical care and to investigate the impact of the exclusion criteria on the case mix, outcomes and length of stay for admissions to intensive care units (ICUs) in England, Wales and Northern Ireland.

However, his engagement with epistemological issues made him dissatisfied with what he had done, so that, when he moved to Bonn, he rethought the problem of theological method in critical discussion with the philosopher of science Heinrich Scholz.

For the proof of Theorem 1.1 we follow the approach of the variational method and use a minimax method in critical point theory on the loop space ΛD, and for the proof of Theorem 1.2 we follow homology theory.

Under the assumptions of Theorem 1.1, we show that the functional (J ucirc x)) satisfies the Palais-Smale condition, so that we can use the variational linking method in critical point theory.

t ∈ [ 0, T ], u ( 0 ) − u ( T ) = u ˙ ( 0 ) − u ˙ ( T ) = 0, where T > 0. Some new existence and multiplicity theorems are obtained by using the least action principle, and the minimax method in critical point theory, which unify and generalize some of the recent corresponding results in the literature.

However, few prospective studies exist comparing the technique itself of ultrasound-guided central venous cannulation versus the landmark method in critical care patients [ 14].

Plans are moving forward to use this study design and methods in other critical care settings.