Sentence examples for existence solutions from inspiring English sources

Many authors have investigated the existence solutions of fractional function equations with impulse [13 18].

Common fixed point theorems have provided powerful tools in demonstrating the existence solutions to large variety of problem in applied mathematics.

The authors got the existence solutions by the method of the fixed point theorem, the coincidence degree theorem, or Schauder's fixed point theorem.

Although the present study provides some insights in the equations encountered in the non-global existence solutions, this existence and uniqueness theorem may be explored for other classes of fractional differential equations which encounter in the global existence solutions, like recent contributions [16, 24], that is a subject for future study.

The obtained results in Theorem 1 can be applied to the study of existence solutions of the initial Cauchy problem for singular linear systems of ordinary differential equations B ( t ) x ˙ = A ( t ) x + f ( t ), t ∈ [ a, b ], (18).

The Sliding Mode Regulation Problem is formulated, and the existence solution conditions are derived.

On the existence solution of ( F, e ) in E 0 ( R ), we establish the following result.

Indeed, we prove the local existence solution for the problem (1.1) by Picard's iteration method.

On the existence solution of ( G, e, q ) in E 0 ( R ), we establish the following result.

We prove an existence result for solutions of (4.1).

Existence of solutions is derived under consistency and regularity of the initial data.