In this paper, we establish a solution to the following integral equation: u ( t ) = ∫ 0 T G ( t, s ) f ( s, u ( s ) ) d s for all t ∈ [ 0, T ], (1).
We establish a result concerning the existence of solutions for the following implicit integral equation:, where is not supposed continuous with respect to the second variable.
In order to test the stability of a learned behaviour in the presence of alternative solutions, we established a group norm by presenting an apparatus that could be opened either by pushing or pulling a door [29] to six free-living family groups.
By some fixed theorems of a sum operator on cone, we establish a unique solution and set up two iterative schemes to approximate the solution.
In this paper, we establish a new solution of the problem (C).
Again, we should establish a solution ( x 1 ( k ), x 2 ( k ) ) of system (7) as in the form of (13).
In Section 4 we established an existence theorem for the solution of an initial value problem, which not only gives the unique solution but also locates the domain for the solution.
In this section, we establish an optimized solution for the BLT problem based on the hybrid algorithm scheme.
Furthermore, we establish a blow-up solution and obtain both upper and lower bounds for the maximum blow-up time under some appropriate hypotheses.
Under suitable assumptions on the initial data and the relaxation function, we establish a blow-up result of a solution for negative initial energy and some positive initial energy if the influence of the source term is greater than the dissipation.
We establish a general existence result for solutions lying in an admissible bounding set for the system of ordinary differential equations (1) satisfying boundary conditions (2) and impulses (3).
