Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator
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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.
CitationMassa, E. (2004). Superlinear equations and a uniform anti-maximum principle for the multi-Laplacian operator. Electronic Journal of Differential Equations, 2004(97), pp. 1-19.
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