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On a Elliptic System Involving Nonhomogeneous Nonlinearities and Critical Growth.
- Source :
- Bulletin of the Brazilian Mathematical Society; Jun2023, Vol. 54 Issue 2, p1-22, 22p
- Publication Year :
- 2023
-
Abstract
- Let Ω ⊂ R N be a bounded domain with N ≥ 3 . We address the existence and nonexistence of solutions for the following class of elliptic systems: - Δ u = a u + b v + μ | u | p - 2 u in Ω - Δ v = b u + a v + | v | 2 ∗ - 2 v in Ω <graphic href="574_2023_337_Article_Equ22.gif"></graphic> with Dirichlet boundary condition, where a , b ∈ R , the exponent p > 1 , μ ∈ R is a parameter and 2 ∗ = 2 N / (N - 2) is the critical Sobolev exponent. By exploiting minimization arguments, minimax techniques and a Pohozaev identity, we obtain various results for the above system by analyzing the interplay between a , b , μ and the exponent p. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16787544
- Volume :
- 54
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Bulletin of the Brazilian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 162692758
- Full Text :
- https://doi.org/10.1007/s00574-023-00337-9