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Two nontrivial solutions for quasilinear periodic equations

Authors: Evgenia H. Papageorgiou and Nikolaos S. Papageorgiou
Journal: Proc. Amer. Math. Soc. 132 (2004), 429-434
MSC (2000): Primary 34B15, 34C25
Published electronically: June 17, 2003
MathSciNet review: 2022365
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Abstract: In this paper we study a nonlinear periodic problem driven by the ordinary scalar p-Laplacian and with a Carathéodory nonlinearity. We establish the existence of at least two nontrivial solutions. Our approach is variational based on the smooth critical point theory and using the ``Second Deformation Theorem".

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  • 1. R. Adams: Sobolev Spaces, Academic Press, New York (1975). MR 56:9247
  • 2. P.Bartolo-V.Benci-D.Fortunato: Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Anal. 7 (1983), 981-1012. MR 85c:58028
  • 3. K.-C. Chang: Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston (1993). MR 94e:58023
  • 4. H.Dang-S.F.Oppenheimer: Existence and uniqueness results for some nonlinear boundary value problems, J. Math. Anal. Appl. 198 (1996), 35-48. MR 96m:34033
  • 5. M.Del Pino-R.Manasevich-A.Murua: Existence and multiplicity of solutions with prescribed period for a second order quasilinear ode, Nonlinear Anal. 18 (1992), 79-92. MR 92m:34055
  • 6. C.Fabry-D.Fayyad: Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities, Rend. Istit. Mat. Univ. Trieste 24 (1992), 207-227. MR 96b:34027
  • 7. Z. Guo: Boundary value problems of a class of quasilinear ordinary differential equations, Diff. Integral Eqns. 6 (1993), 705-719. MR 94d:34029
  • 8. S.Hu-N.S.Papageorgiou: Handbook of Multivalued Analysis. Volume I: Theory, Kluwer, Dordrecht, The Netherlands (1997). MR 98k:47001
  • 9. S.Kyritsi-N.Matzakos-N.S.Papageorgiou: Periodic problems for strongly nonlinear second order differential inclutions, J. Diff. Eqns. 183 (2002), 279-302.
  • 10. R.Manasevich-J.Mawhin: Periodic solutions for nonlinear systems with p-Laplacian like operators, J. Diff. Eqns. 145 (1998), 367-393. MR 99c:34034
  • 11. J. Mawhin: Periodic solutions of systems with $p$-Laplacian-like operators in Nonlinear Analysis and Applications to Differential Equations, Lisbon (1997), Progress in Nonlinear Differential Equations and Applications, Birkhäuser, Boston (1998). MR 2002d:34029
  • 12. J.Mawhin-M.Willem: Critical Point Theory and Hamiltonian Systems, Springer-Verlag, New York (1989). MR 90e:58016
  • 13. M. Struwe: Variational Methods, Springer-Verlag, Berlin (1990). MR 92b:49002

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Additional Information

Evgenia H. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Nikolaos S. Papageorgiou
Affiliation: Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece

Keywords: Ordinary p-Laplacian, critical point, Palais-Smale condition, second deformation theorem, strong deformation retract, strong resonance
Received by editor(s): May 29, 2002
Received by editor(s) in revised form: September 30, 2002
Published electronically: June 17, 2003
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2003 American Mathematical Society

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