We consider elliptic equations in bounded domains Ω ⊃ ℝN with non-linearities 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, similarly as in the famous result of Brezis-Nirenberg for equations with critical growth.
Elliptic equations with one-sided critical growth / M. Calanchi, B. Ruf. - In: ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 1072-6691. - 2002:89(2002), pp. 1-21.
Elliptic equations with one-sided critical growth
M. CalanchiPrimo
;B. RufUltimo
2002
Abstract
We consider elliptic equations in bounded domains Ω ⊃ ℝN with non-linearities 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, similarly as in the famous result of Brezis-Nirenberg for equations with critical growth.
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