Global solution curves for boundary value problems, with linear part at resonance

We study existence and multiplicity of solutions for both Dirichlet and Neumann two-point boundary value problems at resonance. We obtain a detailed picture of the solution set, which, in particular, provides an effective way to compute all of the solutions. Our multiplicity results range from uniqueness to infinite multiplicity. Our approach can be seen as a dynamical version of the classical Liapunov–Schmidt procedure. After decomposing the space, we perform continuation in the subspace orthogonal to the kernel.