Sentence examples for by applying fixed point from inspiring English sources

This difficulty can be avoided by applying fixed point theory.

In Section 4, asymptotic decay estimate of solutions to the cauchy problem (1.1), (1.2) is established by applying fixed point theorem.

We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems.

end{aligned} Here we mention two results from [33] which were proved by applying fixed point theorems due to Altman and Schauder.

Subsequently, the existence of solutions for matrix equations or ordinary differential equations by applying fixed point theorems were presented in [2 7].

The existence of solutions for matrix equations or ordinary differential equations by applying fixed point theorems are presented in [2, 6, 9, 11, 12].

For the sake of applying fixed point theorem on cone, we construct a cone in by (3.8).

Some new existence results of positive solutions are established by applying fixed-point index theory together with comparison theorem.

Finally, the existence of positive solutions for the problem (1.1) is obtained by applying fixed-point index theory.

Some sufficient criteria are obtained for the existence, multiplicity, and nonexistence of positive solutions by applying fixed-point theorems on a convex cone.

The existence and nonexistence of positive solutions were shown by applying Banach fixed point theorem, nonlinear alternative of Leray-Schauder type and the fixed point theorems of cone expansion and compression of norm type.