Multiplicity of Solutions for Doubly Resonant Neumann Problems
Filippakis, Michael E. ; Papageorgiou, Nikolaos S.
Bull. Belg. Math. Soc. Simon Stevin, Tome 18 (2011) no. 1, p. 135-156 / Harvested from Project Euclid
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In this paper,we examine semilinear Neumann problems which at $\pm\infty$ are resonant with respect to two successive eigenvalues (double resonance situation). Using variational methods based on the critical point theory together with Morse theory, we prove two multiplicity results. In the first we obtain two nontrivial solutions and in the second three, two of which have constant sign (one positive, the other negative).
Publié le : 2011-03-15
Classification:  Double resonance,  LL-condition,  Morse theory,  critical groups,  multiple solutions,  35J8015,  35J85,  58E05 
@article{1299766494,
     author = {Filippakis, Michael E. and Papageorgiou, Nikolaos S.},
     title = {Multiplicity of Solutions for Doubly Resonant Neumann Problems},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {18},
     number = {1},
     year = {2011},
     pages = { 135-156},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1299766494}
}

Filippakis, Michael E.; Papageorgiou, Nikolaos S. Multiplicity of Solutions for Doubly Resonant Neumann Problems. Bull. Belg. Math. Soc. Simon Stevin, Tome 18 (2011) no. 1, pp.  135-156. http://gdmltest.u-ga.fr/item/1299766494/