Geodesic
Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator
Electronic Journal of Differential Equations, Tome 2004 (2004).

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

Summary: In the first part of this paper, we study a nonlinear equation with the multi-Laplacian operator, where the nonlinearity intersects all but the first eigenvalue. It is proved that under certain conditions, involving in particular a relation between the spatial dimension and the order of the problem, this equation is solvable for arbitrary forcing terms. The proof uses a generalized Mountain Pass theorem. In the second part, we analyze the relationship between the validity of the above result, the first nontrivial curve of the Fucik spectrum, and a uniform anti-maximum principle for the considered operator.
Classification : 35G30, 49J35
Keywords: higher order elliptic boundary value problem, superlinear equation, mountain pass theorem, anti-maximum principle 
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     author = {Massa, Eugenio},
     title = {Superlinear equations and a uniform anti-maximum principle for the {multi-Laplacian} operator},
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     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a87/}
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Massa, Eugenio. Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a87/