Calanchi, MartaRuf, Bernhard2020-08-182020-08-182002-10-18Calanchi, M., & Ruf, B. (2002). Elliptic equations with one-sided critical growth. <i>Electronic Journal of Differential Equations, 2002</i>(89), pp. 1-21.1072-6691https://hdl.handle.net/10877/12422We consider elliptic equations in bounded domains Ω ⊂ ℝN with nonlinearities which have critical growth at +∞ and linear growth λ at -∞, with λ > λ1, the first eigenvalue of the Laplacian. We prove that such equations have at least two solutions for certain forcing terms provided N ≥ 6. In dimensions N = 3, 4, 5 an additional lower order growth term has to be added to the nonlinearity, similarity as in the famous result of Brezis-Nirenberg for equations with critical growth.Text21 pages1 file (.pdf)enAttribution 4.0 InternationalNonlinear elliptic equationCritical growthLinking structureArticle