Resonant semilinear problems with nonlinear term depending on the derivative ✩

We study the existence of solution for a boundary value problem at resonance where the nonlinearity depends only on the derivative. In a sense, we can say that the problem considered is strongly resonant. Our proofs make use of the Lyapunov–Schmidt reduction; in so doing, we are led with the asymptotic estimate of the corresponding bifurcation equation.  2004 Elsevier Inc. All rights reserved