Sentence examples for establish new solutions from inspiring English sources

This method is powerful, efficient, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.

We have been testing and poking our way into establishing new solutions to old problems and, as consumers, we have embraced more new technologies than ever before.

In this section, we establish new oscillation criteria for solutions of equation (1.1).

In the following theorem, by using the results of Dzurina [3], we will establish new oscillation criteria for solutions of equation (1.1) under the conditions int_{tau_{0}}^{infty}frac{s^{2}}{r^{1/alpha} ( s ) },ds=infty quadtext{and}quad int_{tau_{0}}^{infty}R_{2} ( s ),ds=infty.

Also, Özbekler et al. [14] made use of the concept of nonprinciple solutions to establish new oscillation criteria.

In the next, we consider separately delay and advanced cases of the argument deviation to establish new sufficient conditions for all solutions of (1.1) to have property B (see Definition 1).

Therefore, it is of special interest to establish new criteria ensuring oscillation of all solutions of (1.1) when (tau(t)< t).

With potential for cost reductions as standards mature, Web services products and technologies are now being assembled to create working solutions and to establish new business models.

But even with this apparently de-structured approach the "garbage can" model was not only a descriptive tool, a number of prescriptive implications could be derived from it: work on problem re-definition; try to bring in new actors; try to establish new connections between problem-holders and solutions providers; renounce to any comprehensive treatment.

By using the coincidence degree theory, we establish new results on the existence of periodic solutions for the above equation.

We establish new bounds of the Sobolev norms of the solution.