Geodesic
A generalization of the Landesman-Lazer condition
Electronic journal of differential equations, Tome 2001 (2001)
In this paper we prove the existence of solutions to the semi-linear problem

$ \displaylines{ u''(x)+m^2 u(x)+g(x,u(x))=f(x)\cr u(0)=u(\pi)=0 }$

at resonance. We assume a Landesman-Lazer type condition and use a variational method based on the Saddle Point Theorem.
Classification : 35J70, 35P30, 47H15
Keywords: resonance, eigenvalue, landesman-lazer condition 
@article{EJDE_2001__2001__a11,
     author = {Tomiczek,  Petr},
     title = {A generalization of the {Landesman-Lazer} condition},
     journal = {Electronic journal of differential equations},
     year = {2001},
     volume = {2001},
     zbl = {0974.34019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a11/}
}
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Tomiczek,  Petr. A generalization of the Landesman-Lazer condition. Electronic journal of differential equations, Tome 2001 (2001). http://geodesic.mathdoc.fr/item/EJDE_2001__2001__a11/