Sentence examples for by using nonlinear alternative from inspiring English sources

In addition, Agarwal and O'Regan [7] obtained positive solution of second-order right focal BVPs on time scale by using nonlinear alternative of Leray-Schauder type.

We establish sufficient conditions to guarantee the existence of unbounded solution in a special function space by using nonlinear alternative of Leray-Schauder type.

The existence of solutions for problem (3.10) was investigated for convex as well as nonconvex valued maps by using nonlinear alternative of Leray-Schauder type and a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, respectively.

The existence of positive solutions for nonlinear fourth-order multipoint boundary value problems has been studied by many authors using nonlinear alternatives of Leray-Schauder, the fixed point theory, and the method of upper and lower solutions (see, e.g., [1 15] and references therein).

Owing to its significance in physics, the existence of positive solutions for the fourth-order boundary value problem has been studied by many authors using nonlinear alternatives of Leray-Schauder, the fixed point index theory, the Krasnosel'skii's fixed point theorem and the method of upper and lower solutions, in reference [1 10].

This limitation could be addressed by using nonlinear cost functions.

Kinetic parameters were obtained by using nonlinear regression.

The kinetic parameters were refined by using nonlinear regression.

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

Bai et al. [2] obtained the existence of solutions for the BVP (1.1)–(1.3) by using a nonlinear alternative of Leray-Schauder type.

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