Existence of solutions of a second order equation defined on unbounded intervals with integral conditions on the boundary

Abstract

In this paper we shall use the upper and lower solutions method to prove the existence of at least one solution for the second order equation defined on unbounded intervals with integral conditions on the boundary:where m > 0, m = 1 6 , B ∈ R and f : [0, +∞) × R 2 → R is a continuous function satisfying a suitable locally L 1 bounded condition and a kind of Nagumo's condition with respect to the first derivative.

IT2 fuzzy adaptive containment control for fractional-order heterogeneous multi-agent systems with input saturation

“…Although the containment control problem of integer-order multi-agent systems has been widely studied [8][9][10][11][12][13][14][15][16], many physical systems exhibit fractional-order (non-integer) dynamic behaviors due to their unique materials and characteristics, such as microorganisms in under-water environments and unmanned aerial vehicles operating in complex space environments. Compared with integer-order differential equations [17][18][19], fractional-order differential equations have non-local and long-memory effects [20,21], which makes them of great value in studying nonlinear systems, chaotic phenomena, and functional calculus. Therefore, it is important to study the dynamics of multi-agent systems in the sense of fractional-order and to investigate the containment control problem of fractional-order nonlinear systems, which has practical significance [22][23][24][25][26].…”