Existence and location of solutions to fourth-order Lidstone coupled systems with dependence on odd derivatives

Asymptotic properties of PDEs in compact spaces

“…The use of topological methods in the study of PDE is a classical field of research-see [15,16,23,29]. Unfortunately, the most modern and sophisticated methods that have been recently developed for ODEs-see, for instance, [1,3,27,38]-have been difficult to apply to PDEs. The reasons for this are, to cite some, the greater effort needed to check the, if rather weak, cumbersome hypotheses, the lower availability of explicit expressions of Green's functions for PDEs, the higher complexity of the domain of definition and the higher regularity that is necessary in order to obtain existence and uniqueness results.…”