Geodesic
Solution to a semilinear problem on type II regions determined by the Fučik spectrum
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     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},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     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/