
Journal of Convex Analysis 24 (2017), No. 3, 769793 Copyright 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 1764, 014700 Bucharest, Romania vicentiu.radulescu@imar.ro [Abstractpdf] 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 AmbrosettiRabinowitz 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 [ Fulltextpdf (205 KB)] for subscribers only. 