Geodesic
Solution to a semilinear problem on type II regions determined by the Fučik spectrum
Electronic journal of differential equations, Tome 2003 (2003)
We prove the existence of solutions to the semi-linear problem

$\displaylines{ u''(x)+\alpha u^+(x)+\beta u^-(x)=f(x)\,,\quad x\in (0,\pi)\,,\cr u(0)=u(\pi)=0 } $

where the point $(\alpha,\beta)$ falls in regions of type (II) between curves of the Fucik spectrum. We use a variational method based on the generalization of the Saddle Point Theorem.
Classification : 35J70, 58E05, 49B27
Keywords: resonance, eigenvalue, jumping nonlinearities, Fucik spectrum 
@article{EJDE_2003__2003__a196,
     author = {Tomiczek,  Petr},
     title = {Solution to a semilinear problem on type {II} regions determined by the {Fu\v{c}ik} spectrum},
     journal = {Electronic journal of differential equations},
     year = {2003},
     volume = {2003},
     zbl = {1088.35027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a196/}
}
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Tomiczek,  Petr. Solution to a semilinear problem on type II regions determined by the Fučik spectrum. Electronic journal of differential equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a196/