NEW RESULTS ON K- STABILITY AND BOUNDEDNESS OF SOLUTIONS OF A CERTAIN DIFFERENTIAL EQUATIONS IN BANACH SPACES INTERACTING WITH WEAKLY SUBSYSTEMS
E. P. EBIENDELE *
Department of Basic Sciences, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
F. U. NOSAKHARE
Department of Basic Sciences, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
A. A. MOMOH
Department of Basic Sciences, School of General Studies, Federal Polytechnic, Auchi, Edo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The article gives new results of K- Stability and Boundedness of solutions of certain differential equations in Banach Spaces interacting with weakly subsystems. Some results from the theory of semigroups, and the description of the general method of solution of the posed problem were also given. The application of the matrix – valued Lyapunov function is discussed and the main theorem of the method is formulated for differential equations in a Banach Space. The vector Lyapunov function was the main tool applied for the analysis of K – Stability and Boundedness of a system in Banach Spaces. All the results of this Article for the ‘equation (2.2)’ are essentially new.
Keywords: New results, k- stability, bounded solutions, weakly systems, differential equations