Sentence examples for by using some fixed-point from inspiring English sources

By using some fixed-point theorems and some properties of the Green function, the existence of positive solutions was obtained.

They obtained the existence and multiplicity results of positive solutions by using some fixed point theorems.

By using some fixed point theorems, they obtained the existence and multiplicity result of positive solution to this problem.

By using some fixed point index theorems on a cone for differentiable operators, the authors obtain the existence of positive solutions to the above boundary value problem.

By using some fixed point theorems, the existence theorems of mild solutions are obtained, our results are also more general than some well-known results.

By using some fixed point theorems, they obtained the existence, uniqueness and multiplicity of positive solutions to singular positone and semipositone problems.

The purpose is to establish sufficient conditions on the existence of positive solutions to (1.1) by using some fixed point theorems and some properties of the Green function.

For instance, by using some fixed point theorems on cones associated with some properties of the Green's function, several existence results of positive solution for nonlinear q-fractional boundary value problem are obtained by Liu [26].

The purpose here is to establish the existence-uniqueness of positive solutions to the singular Dirichlet problem for the Lane-Emden-Fowler equation (3.3) by using some fixed point results in Section 2.

In this paper, by using some fixed point theorems and the measure of noncompactness, we discuss the existence of solutions for a boundary value problem of impulsive integrodifferential equations of fractional order (alphain(1,2]).

Recently, the existence and multiplicity of positive periodic solutions for a scalar singular equation or singular systems have been studied by using some fixed point theorems; see [1 9].