Sentence examples for minimal solutions for from inspiring English sources

In this section, we consider the existence of maximal and minimal solutions for (1.2).

Moreover, the existence of maximal and minimal solutions for the problem is also given.

In this section, we shall prove the existence of maximal and minimal solutions for BVPHDEF (1) on (J = [0, T ]).

In this section, we prove the existence of maximal and minimal solutions for FHDE (2.1) on J = [ t 0, t 0 + a ].

The existence of maximal and minimal solutions for (1.2) is given in Section 4. For the convenience of the reader, we present here the necessary definitions and properties from fractional calculus theory, which are used throughout this paper.

In this article, we establish the extreme solutions (maximal and minimal solutions) for fractional differential equation with maxima in sense of Riemann-Liouville fractional operators, by using the Tarski's fixed point theorem.

Although mathematical solutions for specific boundaries had been obtained through the years, it was not until 1931 that Douglas (and independently the Hungarian American mathematician Tibor Radó) first proved the existence of a minimal solution for any given "simple" boundary.

Although mathematical solutions for specific boundaries had been obtained through the years, it was not until 1931 that the American mathematician Jesse Douglas (and independently the Hungarian American mathematician Tibor Radó) first proved the existence of a minimal solution for any given "simple" boundary.

}t in J, x (t_{0}) = x_{0} inmathbb{R}, end{cases} where (J=[t_{0},t_{0}+a)), in (mathbb{R}) for some fixed (t_{0},a inmathbb {R}) with (a > 0), and (f, g inmathcal{C}(Jtimesmathbb{R}, mathbb{R})). They proved the existence of the maximal and minimal solution for this equation.

We focus on the "minimal solution" for each ammonium concentration.

EEEP successfully returned the minimal solution for all tests with three or less RSPRs or four RSPRs and ten leaves.