Elliptic equations with one-sided critical growth
We consider elliptic equations in bounded domains $Omegasubset 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...
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Texas State University
2002-10-01
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doaj-ae9ae175ed60428ea1ca2d83cb2658082020-11-24T23:04:16ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912002-10-01200289121Elliptic equations with one-sided critical growthMarta CalanchiBernhard RufWe consider elliptic equations in bounded domains $Omegasubset 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 $N ge 6$. 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. Submitted March 01, 2002. Published October 18, 2002. Math Subject Classifications: 35J20. Key Words: Nonlinear elliptic equation; critical growth; linking structure. http://ejde.math.txstate.edu/Volumes/2002/89/abstr.htmlNonlinear elliptic equationcritical growthlinking structure. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Marta Calanchi Bernhard Ruf |
spellingShingle |
Marta Calanchi Bernhard Ruf Elliptic equations with one-sided critical growth Electronic Journal of Differential Equations Nonlinear elliptic equation critical growth linking structure. |
author_facet |
Marta Calanchi Bernhard Ruf |
author_sort |
Marta Calanchi |
title |
Elliptic equations with one-sided critical growth |
title_short |
Elliptic equations with one-sided critical growth |
title_full |
Elliptic equations with one-sided critical growth |
title_fullStr |
Elliptic equations with one-sided critical growth |
title_full_unstemmed |
Elliptic equations with one-sided critical growth |
title_sort |
elliptic equations with one-sided critical growth |
publisher |
Texas State University |
series |
Electronic Journal of Differential Equations |
issn |
1072-6691 |
publishDate |
2002-10-01 |
description |
We consider elliptic equations in bounded domains $Omegasubset 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 $N ge 6$. 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. Submitted March 01, 2002. Published October 18, 2002. Math Subject Classifications: 35J20. Key Words: Nonlinear elliptic equation; critical growth; linking structure. |
topic |
Nonlinear elliptic equation critical growth linking structure. |
url |
http://ejde.math.txstate.edu/Volumes/2002/89/abstr.html |
work_keys_str_mv |
AT martacalanchi ellipticequationswithonesidedcriticalgrowth AT bernhardruf ellipticequationswithonesidedcriticalgrowth |
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1725631618763194368 |