Elliptic Equations with One-sided Critical Growth

Date

2002-10-18

Authors

Calanchi, Marta
Ruf, Bernhard

Journal Title

Journal ISSN

Volume Title

Publisher

Southwest Texas State University, Department of Mathematics

Abstract

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.

Description

Keywords

Nonlinear elliptic equation, Critical growth, Linking structure

Citation

Calanchi, M., & Ruf, B. (2002). Elliptic equations with one-sided critical growth. <i>Electronic Journal of Differential Equations, 2002</i>(89), pp. 1-21.

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Attribution 4.0 International

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