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scalar p-laplacian

Proceedings of the Edinburgh Mathematical Society (1)

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Solutions and multiple solutions for superlinear perturbations of the periodic scalar p-Laplacian
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Sophia Th. Kyritsi, Donal O'Regan, Nikolaos S. Papageorgiou
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013

Published online by Cambridge University Press:

28 June 2013, pp. 805-827
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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).