Sentence examples for solutions methods to from inspiring English sources

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

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

We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of radially symmetric positive solutions.

In the last section, we apply the fixed point index theory and the upper and lower solutions method to prove the main result.

Hence, we propose a new analogue of the operator Φ and apply the fixed point index theory combining with the upper and lower solutions method to investigate the multiplicity of positive radially symmetric solutions for the problem (P).

Wei et al. [22] applied chemical solution methods to synthesize cuprous-oxide (Cu2O) nanoparticles in water, to form Cu2O nanofluids.

Many authors studied and constructed some solution methods to solve the GMEP θ, A, φ), MEP, EP [[1 16], and references therein].

In the literature, one can find a variety of bi-dimensional theories and solution methods to solve these problems.

We present two solution methods to solve the problem with one returning heuristic solutions and the other generating a globally optimal solution.

This section presents a fair comparison between the two solution methods, to compare the numerical results generated by the proposed NSGA-II and ɛ-Constraint proposed here.

A 4-Factor Design of Experiments is conducted to investigate the optimality of each solution methods to different URT line characteristics.