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Elliptic equations with one-sided critical growth. (English) Zbl 1022.35009
Authors’ summary: We consider elliptic equations in bounded domains $$\Omega\subset \mathbb{R}^N$$ with nonlinearities which have critical growth at $$+\infty$$ and linear growth $$\lambda$$ at $$-\infty$$, with $$\lambda > \lambda_1$$, the first eigenvalue of the Laplacian. We prove that such equations have at least two solutions for certain forcing terms provided $$N \geq 6$$. 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.
Reviewer: V.Mustonen (Oulu)

##### MSC:
 35J20 Variational methods for second-order elliptic equations 35J60 Nonlinear elliptic equations
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