Elliptic Equations with One-sided Critical Growth
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We 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.
CitationCalanchi, M., & Ruf, B. (2002). Elliptic equations with one-sided critical growth. Electronic Journal of Differential Equations, 2002(89), pp. 1-21.
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