Sentence examples for methods they obtained from inspiring English sources
When they applied these methods, they obtained the opposite result to previous studies -- that most people actually weren't psychologically resilient.
By applying the critical point theorem and variational methods, they obtained the existence results of at least one and three solutions for problem (1.2).
Under suitable hypotheses and by applying variational methods, they obtained some new criteria guaranteeing that the studied systems have at least two nontrivial and nonnegative solutions.
By using topological degree methods they obtained that a necessary and sufficient condition for the existence of positive periodic solutions for equation (1.1) is (overline{h}>0), and if we assume in addition that (alpha ge 1), then a necessary and sufficient condition for the existence of positive periodic solutions for equation (1.2) is (overline{h}<0).
Using these optical constants and the DDA method, they obtained the extinction spectra for parallelepiped shapes with various edges ratios.
By virtue of the upper-lower solution method, they obtained the existence of global solutions, blow-up properties and blow-up rate of the solutions.
By using a scalarization method, they obtained the lower semicontinuity of an approximate solution mapping for such a problem without the assumptions of monotonicity and compactness.
By using the well-known Schauder fixed point theorem and upper and lower solution method, they obtained some new existence criteria for positive solutions of the boundary value problem.
However, the study of positive solutions for the semipositone Neumann problems (1.1 - 1.2 1.1 - 1.2isely relativelyMiciano and Shivaji in [8], by using the quadrarere method (time map method), they obtained the following reseet when f has the only unique positive zero.
With this method they obtained diamonds with an average size of 15 nm.
Muroya et al. [22] proposed a discrete epidemic model for a disease with immunity and latency spreading in a heterogeneous host population, which was derived from the continuous case by using the well-known backward Euler method, and they obtained the result of the global stability of the disease-free equilibrium and the endemic equilibrium.
