Bifurcation of limit cycles from an n-dimensional linear center inside a class of piecewise linear differential systems

Let n be an even integer. We study the bifurcation of limit cycles from the periodic orbits of the n-dimensional linear center given by the differential system x1=-x2,x2=x1,⋯,x n-1=-xn,xn=xn-1, perturbed inside a class of piecewise linear differential systems. Our main result shows that at most (4n-6)n2-1 limit cycles can bifurcate up to first-order expansion of the displacement function with respect to a small parameter. For proving this result we use the averaging theory in a form where the differentiability of the system is not needed. © 2011 Elsevier Ltd. All rights reserved.