On resonant Neumann problems (Q1938424)

The authors consider semilinear Neumann elliptic problems, defined on a bounded domain with a smooth boundary. By combining minimax methods based on the critical point theory with techniques from the Morse Theory, they prove the existence of a nontrivial solution for resonant problems with respect to any eigenvalue of the negative Neumann Laplacian, and they present multiplicity results for resonant problems to the first two eigenvalues.