Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 97, pp. 1-19.
Title: Superlinear equations and a uniform anti-maximum principle
for the multi-Laplacian operator
Author: Eugenio Massa (Univ. degli Studi, Milano, Italy)
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.