On an Ambrosetti-Prodi type problem for a class of fourth-order ODEs involving Dirac weights (Q6592257)

The paper deals with the construction of an Ambrosetti-Prodi type result for a general class of fourth-order differential equations involving Dirichlet weights. As stated in the paper, the classical Ambrosetti-Prodi problem studies how perturbations of the linear Dirichlet Laplace operator interact with a nonlinear reaction, especially when the derivative jumps over the principal eigenvalue of the operator. By using the sub-super solution method and Leray-Schauder topological degree theory, the authors investigate the existence/ nonexistence of the solutions. Since it is stated that there are very few studies of this type for fourth-order equations in the literature, it is a valuable study in terms of filling the gap in the literature.