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.