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  • Proceedings of the Edinburgh Mathematical Society, Volume 56, Issue 3
  • October 2013, pp. 805-827

Solutions and multiple solutions for superlinear perturbations of the periodic scalar p-Laplacian

  • Sophia Th. Kyritsi (a1), Donal O'Regan (a2) and Nikolaos S. Papageorgiou (a3)
  • DOI: http://dx.doi.org/10.1017/S0013091513000370
  • Published online: 28 June 2013
Abstract
Abstract

We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a reaction term which exhibits a (p – 1)-superlinear growth near ±∞ but need not satisfy the Ambrosetti-Rabinowitz condition. Combining critical point theory with Morse theory we prove an existence theorem. Then, using variational methods together with truncation techniques, we prove a multiplicity theorem establishing the existence of at least five non-trivial solutions, with precise sign information for all of them (two positive solutions, two negative solutions and a nodal (sign changing) solution).

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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