Strong resonance problems for the one-dimensional p-Laplacian

Abstract

We study the existence of the weak solution of the nonlinear boundary-value problem

-(vertical bar u'vertical bar(p-2)u')' = lambda vertical bar u vertical bar(p-2)u + g(u) - h(x) in (0, pi), u(0) = u(pi) = 0,

where p and lambda are real numbers, p > 1, h is an element of L-p' (0, pi) (p' = p/p-1) and the nonlinearity g : R -> R is a continuous function of the Landesman-Lazer type. Our sufficiency conditions generalize the results published previously about the solvability of this problem.