Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 24 (2017), No. 3, 769--793Copyright Heldermann Verlag 2017 Asymmetric, Noncoercive, Superlinear (p,2)-Equations Nikolaos S. Papageorgiou Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece npapg@math.ntua.gr Vicentiu D. Radulescu Institute of Mathematics, Romanian Academy of Sciences, P. O. Box 1-764, 014700 Bucharest, Romania vicentiu.radulescu@imar.ro [Abstract-pdf] We examine a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a $p$-Laplacian $(p\geq 2)$ and a Laplacian (a $(p,2)$-equation). The reaction term is asymmetric and it is superlinear in the positive direction and sublinear in the negative direction. The superlinearity is not expressed using the Ambrosetti-Rabinowitz condition, while the asymptotic behavior as $x\rightarrow-\infty$ permits resonance with respect to any nonprincipal eigenvalue of $(-\Delta_p,W^{1,p}_{0}(\Omega))$. Using variational methods based on the critical point theory and Morse theory (critical groups), we prove a multiplicity theorem producing three nontrivial solutions. Keywords: (p,2)-equation, asymmetric reaction, superlinear growth, multiple solutions, nonlinear regularity, critical groups. MSC: 35J20, 35J60, 58E05 [ Fulltext-pdf  (205  KB)] for subscribers only.