Geodesic
Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator
Electronic journal of differential equations, Tome 2004 (2004)
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 
@article{EJDE_2004__2004__a87,
     author = {Massa,  Eugenio},
     title = {Superlinear equations and a uniform anti-maximum principle for the {multi-Laplacian} operator},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1109.35353},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a87/}
}
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%J Electronic journal of differential equations
%D 2004
%V 2004
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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/