Dip. di Matematica, Universita degli Studi
Via Saldini 50
20133 Milano, Italy
email: eugenio@mat.unimi.it
Eugenio Massa
Abstract:
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.
Submitted May 25, 2004. Published August 7, 2004.
Math Subject Classifications: 35G30, 49J35.
Key Words: Higher order elliptic boundary value problem;
superlinear equation; mountain pass theorem; anti-maximum principle.
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Eugenio Massa Dip. di Matematica, Universita degli Studi Via Saldini 50 20133 Milano, Italy email: eugenio@mat.unimi.it |
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