Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator
Date
2004-08-07
Authors
Massa, Eugenio
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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.
Description
Keywords
Higher order elliptic boundary value problem, Superlinear equation, Mountain Pass Theorem, Anti-maximum principle
Citation
Massa, E. (2004). Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator. <i>Electronic Journal of Differential Equations, 2004</i>(97), pp. 1-19.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.