Sentence examples for solution has been given from inspiring English sources

Recently, the special linear case of (psi x,varphi(x))=q(x varphi(x)) has been studied in [28] and an approximate solution has been given.

In their work, the discontinuity in the first derivative at its peak of the soliton solution has been given as a limiting form.

The range of applicability and limitations of the proposed solution has been given, as well as the benefits from the application.

The case of (g(x)=0) in equation (1) with impulse three-point boundary value conditions have been studied in [29], where the existence conditions for obtaining a nontrivial solution have been given.

Analytical solutions have been given wherever possible.

The sufficient conditions for the existence of solutions and nonnegative solutions have been given.

Based on the Schauder fixed point theorem, the sufficient conditions for the existence of the solutions have been given.

While limiting-equilibrium Mononobe Okabe type solutions are still widely used in designing rigid gravity and flexible cantilever retaining walls against earthquakes, elasticity-based solutions have been given a new impetus following the analytical work of Veletsos and Younan [23].

The first steps in the theory of lower and upper solutions have been given by Picard in 1890 [1] for Partial Differential Equations and, three years after, in [2] for Ordinary Differential Equations.

Recently, a large of generalized vector equilibrium problems have been studied in different conditions by many authors and a lot of results concerned with the existence of solutions and properties of solutions have been given in finite and infinite dimensional spaces (see [7] and the references therein).

The existence and uniqueness for the solution of WSIAEs has been given in [11, 12].