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Volume 24, Issue 4
Nonradial Solutions of a Mixed Concave-convex Elliptic Problem

Anouar Ben Mabrouk & Mohamed Lakdar Ben Mohamed

DOI: 10.4208/jpde.v24.n4.3

J. Part. Diff. Eq., 24 (2011), pp. 313-323.

Published online: 2011-11

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  • Abstract

We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.

  • Keywords

Group invariance nonlinear elliptic equations variational method Brezis-Nirenberg problem eigenvalue and eigenfunction problems

  • AMS Subject Headings

35J60 35B05 35P30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-313, author = {Anouar Ben Mabrouk and Mohamed Lakdar Ben Mohamed }, title = {Nonradial Solutions of a Mixed Concave-convex Elliptic Problem}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {4}, pages = {313--323}, abstract = {

We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n4.3}, url = {http://global-sci.org/intro/article_detail/jpde/5213.html} }
TY - JOUR T1 - Nonradial Solutions of a Mixed Concave-convex Elliptic Problem AU - Anouar Ben Mabrouk & Mohamed Lakdar Ben Mohamed JO - Journal of Partial Differential Equations VL - 4 SP - 313 EP - 323 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.3 UR - https://global-sci.org/intro/article_detail/jpde/5213.html KW - Group invariance KW - nonlinear elliptic equations KW - variational method KW - Brezis-Nirenberg problem KW - eigenvalue and eigenfunction problems AB -

We study the homogeneous Dirichlet problem in a ball for semi-linear elliptic problems derived from the Brezis-Nirenberg one with concave-convex nonlinearities. We are interested in determining non-radial solutions which are invariant with respect to some subgroup of the orthogonal group. We prove that unlike separated nonlinearities, there are two types of solutions, one converging to zero and one diverging. We conclude at the end on the classification of non radial solutions related to the nonlinearity used.

Anouar Ben Mabrouk and Mohamed Lakdar Ben Mohamed . (2011). Nonradial Solutions of a Mixed Concave-convex Elliptic Problem. Journal of Partial Differential Equations. 24 (4). 313-323. doi:10.4208/jpde.v24.n4.3
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