Nonhomogeneous nonlinear Dirichlet problems with a \(p\)-superlinear reaction (Q437660)

Summary: We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Carathéodory reaction \(f(z, \zeta)\), whose primitive \(f(z, \zeta)\) is \(p\)-superlinear near \(\pm \infty\), but need not to satisfy -- as usual in such cases -- the Ambrosetti-Rabinowitz condition. Using a combination of variational methods with the Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions. Our result unifies the study of ``superlinear'' equations monitored by some differential operators of interest like the \(p\)-Laplacian, the \((p, q)\)-Laplacian, and the \(p\)-generalized mean curvature operator.