Strong resonance problems for the one-dimensional p-Laplacian

Abstract

We study the existence of the weak solution of the nonlinear boundary-value problem -(|u'|p-2u')' = λ|u|p-2u + g(u) - h(x) in (0, π), u(0) = u(π) = 0, where p and λ are real numbers, p > 1, h ∈ Lp' (0, π) (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.