Geodesic
Resonance with respect to the Fučík spectrum
Electronic journal of differential equations, Tome 2000 (2000)
Let

$ Lu = \alpha u^+ - \beta u^- + f(\cdot,u), $

when the homogeneous equation $Lu = \alpha u^+ - \beta u^-$ has non-trivial solutions. Using the computation of degrees that are not necessarily +1 or -1, we present results about the existence of solutions. Our results are illustrated with examples and can be seen as generalizations of Landesman-Lazer conditions. Non-existence results are also given.
Classification : 70K30, 35P30, 35G30
Keywords: resonance, jumping nonlinearity, landesman-lazer conditions 
@article{EJDE_2000__2000__a58,
     author = {Ben-Naoum,  A.K. and Fabry,  C. and Smets,  D.},
     title = {Resonance with respect to the {Fu\v{c}{\'\i}k} spectrum},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0977.70015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a58/}
}
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AU  - Smets,  D.
TI  - Resonance with respect to the Fučík spectrum
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PY  - 2000
VL  - 2000
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LA  - en
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%A Smets,  D.
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%J Electronic journal of differential equations
%D 2000
%V 2000
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%F EJDE_2000__2000__a58
Ben-Naoum,  A.K.; Fabry,  C.; Smets,  D. Resonance with respect to the Fučík spectrum. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a58/