SOLVABILITY FOR SOME DIRICHLET PROBLEM WITH P-LAPACIAN

We investigate the existence of the following Dirichlet boundary value problem (vertical bar u'vertical bar(p-2)u'] + (p-1) [alpha vertical bar u(+)vertical bar(p-2) u(+) - beta vertical bar u(-)vertical bar(p-2) u(-) = (p-1) h(t), u(0) = u(T) = 0, where p >1, alpha > 0, beta > 0 and alpha(-1/p) vertical bar beta(-1/p) = 2, T = pi(P)/alpha(1/p), pi(p) = 2 pi/p sin(pi/p) and h is an element of L-infinity (0, T). The results of this paper generalize some early results obtained in [8] and [9]. Moreover, the method used in this paper is elementary and new.