Sentence examples for solution existence from inspiring English sources

Also, a theorem for optimal solution existence is proposed.

Two necessary and sufficient conditions for the minimal solution existence are given.

The paper studies the question of solution existence to a nonlinear equation in the degenerate case.

Generally, there are mainly two approaches to attack the solution existence problem of the GVI.

A basic theory is presented for determining the solution existence of frequency optimization problems for truss structures.

In the paper, we study the question of solution existence to a nonlinear equation F ( x ) = 0, (1).

We investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant regime; multiple solutions in the resonant regime.

Wang et al. [15, 16] discussed Ulam-Hyers stability for fractional equations and studied several types of such equations with various boundary value conditions as well, concept of solutions, existence results and examples are presented in [17].

Using the method of upper and lower solutions, an existence result of solutions for box integral and differential equations is studied.

Later on, Qin et al. [8, 9] proved the regularity of weak solutions and existence of classical solution.

By constructing upper and lower solutions, the existence of positive solutions for the problem is established.