Geodesic
ON THE MULTIPLICITY OF SOLUTIONS FOR NON-LINEAR PERIODIC PROBLEMS WITH THE NON-LINEARITY CROSSING SEVERAL EIGENVALUES
Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 271-302

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In this paper we consider a non-linear periodic problem driven by the scalar p-Laplacian and with a non-smooth potential. We assume that the multi-valued right-hand-side non-linearity exhibits an asymmetric behaviour at ±∞ and crosses a finite number of eigenvalues as we move from −∞ to +∞. Using a variational approach based on the non-smooth critical-point theory, we show that the problem has at least two non-trivial solutions, one of which has constant sign. For the semi-linear (p = 2), smooth problem, using Morse theory, we show that the problem has at least three non-trivial solutions, again one with constant sign.
DOI : 10.1017/S0017089509990346
Mots-clés : 34B15, 34C25 
KYRITSI, SOPHIA TH.; PAPAGEORGIOU, NIKOLAOS S. ON THE MULTIPLICITY OF SOLUTIONS FOR NON-LINEAR PERIODIC PROBLEMS WITH THE NON-LINEARITY CROSSING SEVERAL EIGENVALUES. Glasgow mathematical journal, Tome 52 (2010) no. 2, pp. 271-302. doi: 10.1017/S0017089509990346
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     title = {ON {THE} {MULTIPLICITY} {OF} {SOLUTIONS} {FOR} {NON-LINEAR} {PERIODIC} {PROBLEMS} {WITH} {THE} {NON-LINEARITY} {CROSSING} {SEVERAL} {EIGENVALUES}},
     journal = {Glasgow mathematical journal},
     pages = {271--302},
     year = {2010},
     volume = {52},
     number = {2},
     doi = {10.1017/S0017089509990346},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990346/}
}
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