Multiplicity theorems for superlinear elliptic problems

  • Nikolaos S. Papageorgiou
  • Eugénio M. Rocha
  • Vasile Staicu


In this paper we study second order elliptic equations driven by the Laplacian and p-Laplacian differential operators and a nonlinearity which is (p-)superlinear (it satisfies the Ambrosetti–Rabinowitz condition). For the p-Laplacian equations we prove the existence of five nontrivial smooth solutions, namely two positive, two negative and a nodal solution. Finally we indicate how in the semilinear case, Morse theory can be used to produce six nontrivial solutions.

Mathematics Subject Classification (2000)

35J20 35J60 58E05 58J70 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Nikolaos S. Papageorgiou
    • 1
  • Eugénio M. Rocha
    • 2
  • Vasile Staicu
    • 2
  1. 1.Department of MathematicsNational Technical UniversityAthensGreece
  2. 2.Department of MathematicsUniversity of AveiroAveiroPortugal

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