Sentence examples for solutions methods from inspiring English sources

So many authors developed the upper and lower solutions methods to solve fractional differential equations; for examples, see [12 26].

(1.2 The methods used in [22] are based upon the growth argument and the upper and lower solutions methods.

How the non-autonomous case affects information propagation and the dynamic properties of solutions over social networks is obtained by upper and lower solutions methods and comparison principle.

subject to (1.2) and (1.3) and proved that the sufficient condition for the extinction to occur is 0 < r < 1 by using the upper and lower solutions methods.

These classical techniques contain fixed point theory, topological degree theory and comparison method (including monotone iterative method and upper and lower solutions methods).

Our proofs are based on the method of global continuous theorem, the lower-upper solutions methods and fixed point index theory.

We give a fundamental lemma of upper and lower solutions method.

The arguments used rely on the upper and lower solutions method (see [1, 2]).

The main techniques are Schauder fixed point theorem and upper and lower solutions method.

In [6, 18], some solution methods are proposed.

Many solution methods work only with single objectives.