On a Robin problem with p-Laplacian and reaction bounded only from above

الأصل · EN

The existence of three smooth solutions, one negative, one positive, and one nodal, to a homogeneous Robin problem with p-Laplacian and Carathéodory reaction is established. No sub-critical growth condition is taken on. Proofs exploit variational as well as truncation techniques. The case p=2 is separately examined, obtaining a further nodal solution via Morse's theory.