Abstract

We examine a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a pp-Laplacian (p≥2)(p\geq 2) and a Laplacian (a (p,2)(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→−∞x\rightarrow-\infty permits resonance with respect to any nonprincipal eigenvalue of (−Δp,W01,p(Ω))(-\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.

Author information

Contact details are reproduced from the original publication and may be historical.

Nikolaos S. Papageorgiou

Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
and: King Saud University, Department of Mathematics, P.O. Box 2454, Riyadh 11451, Kingdom of Saudi Arabia

npapg@math.ntua.gr

Vicenţiu D. Rădulescu

Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Kingdom of Saudi Arabia
and: Institute of Mathematics, Romanian Academy of Sciences, P. O. Box 1-764, 014700 Bucharest, Romania

vicentiu.radulescu@imar.ro

Keywords

  • (p
  • 2)-equation
  • asymmetric reaction
  • superlinear growth
  • multiple solutions
  • nonlinear regularity
  • critical groups

Mathematics Subject Classification

35J20, 35J60, 58E05

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Suggested citation

N. S. Papageorgiou, V. D. Rădulescu. “Asymmetric, Noncoercive, Superlinear (p,2)-Equations.” Journal of Convex Analysis 24 (2017), No. 3, 769–793. https://doi.org/10.68381/jca24047

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