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.
Rights
Attribution 4.0 International