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We consider nonlinear Dirichlet problems driven by the sum of a -Laplacian and a Laplacian and with a Carathéodory reaction which does not satisfy any global growth condition. Instead we assume that it has constant sign -dependent zeros. Using variational methods, truncation techniques and Morse theory, we prove multiplicity theorems providing sign information for all the solutions.
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Leszek Gasiński, Liliana Klimczak, Nikolaos S. Papageorgiou, Nonlinear Dirichlet Problems with no Growth Restriction on the Reaction. Z. Anal. Anwend. 36 (2017), no. 2, pp. 209–238DOI 10.4171/ZAA/1586