Sign-changing solutions for resonant Neumann problems

We consider semilinear Neumann problems at resonance. We are concerned with two distinct cases. In the first one, the potential function is unbounded and indefinite. In the second case, the potential function is bounded and the reaction exhibits a concave parametric term near the origin. We prove two existence theorems producing sign-changing solutions. The first main result is a complement of the results obtained by Papageorgiou and Rădulescu (2015) [22]. The second theorem gives an answer to the open question raised by Candito et al. (2016) [4]. Our approach uses variational methods together with flow invariance arguments.