Sentence examples for minimal nonnegative solution from inspiring English sources

Then problem (1.5) has the minimal nonnegative solution with, where is defined as in Lemma 2.3.

In this section, we establish the existence of a minimal nonnegative solution for problem (1.5).

Traditional approaches for finding its minimal nonnegative solution are based on fixed point iterations and the speed of the convergence is linear.

Then IBVP (1.1) has the minimal nonnegative solution x̅ with (|overline{x}|leqfrac{B}{1-A}), where A and B are defined as in Lemma  2.8.

To establish the existence of minimal nonnegative solution in of problem (1.5), let us list the following assumptions, which will stand throughout this paper.

Based on the cone theory and monotone iterative technique, we establish the existence of minimal nonnegative solution and iteration of positive solutions for such a boundary value problem.

By means of a fixed point theorem of increasing operators, the minimal and maximal nonnegative solutions for the problem are obtained.

As a result, the minimal and maximal nonnegative solutions for the problem are obtained by using a fixed point theorem of increasing operators.

But in [8], Wang obtained the minimal and maximal nonnegative solutions for a second-order m-point boundary value problem at resonance by using a new fixed point theorem of increasing operators, and in this paper we use this method of Wang to establish the existence theorem of equations (1.1) and (1.2).

Therefore, (3.9) has another nonnegative solution u ˜.

Moreover, is a nonnegative solution to (2.19).