Sentence examples for minimum solutions for from inspiring English sources

In the end, we prove that (x^) and (y^) are maximum and minimum solutions for system (1.1).

In this work, we have established an existence result on the maximum and minimum solutions for a class of fractional order differential systems involving a p-Laplacian operator and nonlocal boundary conditions.

In our simulations, we tested both Boltzmann annealing (BA) and fast annealing (FA) temperature cooling schedules which have been proven to provide global minimum solutions for a wide range of problems [23, 24].

Thus, motivated by the above work, in this paper, we consider the maximum and minimum solutions for a fractional order p-Laplacian system subject to a nonlocal Riemann-Stieltjes integral boundary condition.

This paper focuses on the maximum and minimum solutions for a fractional order differential system, involving a p-Laplacian operator and nonlocal boundary conditions, which arises from many complex processes such as ecological economy phenomena and diffusive interaction.

The solution to problem (7) does not guarantee a global minimum solution for problem (6).

Later Lepeltier and San Martin [12] provided an existence result of minimum solution for one-dimensional BSDE where the generator function f is continuous and of linear growth in terms of ((y, z)).

This limitation had led the researchers to explore the application of artificial intelligence based optimization algorithms for obtaining the global minima solution for relay coordination problems.

Finally, the set of rates corresponding to the minimum solution of μ was chosen for further calculation (r and c > 0).

For our special case, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibria problem; the minimum norm solution of the system of mixed type equilibria problem.

For the special case of our results, our results can be reduced to the following problems: the unique minimal norm solution of the multiply sets split monotonic variational inclusion problems; the minimum norm solutions for the multiple sets split system of mixed type equilibrium problem; the minimum norm solution of the system of the mixed type equilibria problem.