Resonant Neumann equations with indefinite linear part

Roberto Livrea, Nikolaos S. Papageorgiou, Giuseppina Barletta



We consider aseminonlinear Neumann problem driven by the $p$-Laplacian plus an indefinite and unbounded potential. The reaction of the problem is resonant at $\pm \infty$ with respect to the higher parts of the spectrum. Using critical point theory, truncation and perturbation techniques, Morse theory and the reduction method, we prove two multiplicity theorems. One produces three nontrivial smooth solutions and the second four nontrivial smooth solutions.


Resonant equation; critical groups; reduction method; multiple solutions; unique continuation property

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