Resonance problems for p-Laplacian

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 results generalize previously published results about the solvability of our problem.