Massa, Eugenio2021-04-262021-04-262004-08-07Massa, 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. 1-19.1072-6691https://hdl.handle.net/10877/13451In 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.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalHigher order elliptic boundary value problemSuperlinear equationMountain Pass TheoremAnti-maximum principleArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.