Sentence examples for solutions method from inspiring English sources

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 [18, 19], some existence results were established by the upper and lower solutions method.

The main tool to obtain the location part is the upper and lower solutions method.

We will apply the subsuper solutions method to prove the multiplicity results.

Now, we will establish the classical lower and upper solutions method for our problem.

We develop some mathematical techniques (including upper and lower solutions method, comparison principle, and the like) for overcoming these difficulties.

Firstly, by the upper and lower solutions method, we investigate the basic existence of positive solutions of problem (1.1 - 1.2 1.1 - 1.2

We will rely on the nonlinear alternative of Leray-Schauder type combined with a lower and upper solutions method.

The proof is based on the fixed-point theorem, the upper-lower solutions method, and the fixed-point index.