BOUNDEDNESS FOR SECOND ORDER DIFFERENTIAL EQUATIONS WITH JUMPING p-LAPLACIAN AND AN OSCILLATING TERM

In this paper, we are concerned with the boundedness of all the solutions for a kind of second order differential equations with p-Laplacian and an oscillating term (phi(p)(x'))' + a phi(p)(x(+)) - b phi(p)(x(-)) = G(x)(x, t) + f(t), where x(+) = max(x, 0), x(-) = max(-x, 0), phi(p)(s) = vertical bar s vertical bar(p-2)s, p >= 2, a and b are positive constants (a not equal b), the perturbation f(t) is an element of C-23(R/2 pi(p)Z), the oscillating term G is an element of C-21(R x R/2 pi(p)Z) satisfying vertical bar D(x)(i)D(t)(j)G(x, t) <= C, 0 <= i + j <= 21.