Sentence examples for using the nonlinear alternative from inspiring English sources

We establish an existence result using the nonlinear alternative of Leray-Schauder type.

Next we give an existence result using the nonlinear alternative of Leray-Schauder.

The existence of nontrivial solution was established by using the nonlinear alternative of Leray-Schauder.

We establish new existence results, when the right hand side is convex valued, by using the nonlinear alternative of Leray-Schauder type.

It is worth noticing that there are a few authors addressing the fractional p-Laplacian problems by using the nonlinear alternative of Leray-Schauder.

The paper [21] obtained the existence of one solution to problem (1.2) by using the nonlinear alternative of Leray-Schauder type.

We use the nonlinear alternative of Schaefer's type due to Dhage [27].

We use the nonlinear alternative of Leray-Schauder and the Banach contraction mapping principle to obtain the existence and uniqueness of solutions.

In this position, we shall use the nonlinear alternative of Leray-Schauder type in order to show that the operator (mathcal{N}) has fixed points.

In this work, we use the nonlinear alternative of Leray-Schauder and give the existence of a solution and its localization.

In the proof of our main results we shall use the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem presented below (see [14, 15]).