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- Title
On the system of p-Laplacian equations with critical growth.
- Authors
Liu, Xiangqing; Zhao, Junfang; Liu, Jiaquan
- Abstract
In this paper, we consider the system of p -Laplacian equations with critical growth − Δ p u j = μ j | u j | p − 2 u j + ∑ i = 1 k β i j | u i | p ∗ 2 | u j | p ∗ 2 − 2 u j , in Ω , u j = 0 , on ∂ Ω , j = 1 , ... , k , where Ω is a bounded smooth domain in ℝ N , 1 < p < N , p ∗ = N p N − p > 2 , 0 < μ j < λ 1 (Ω) the first eigenvalue of the p -Laplacian operator − Δ p with the Dirichlet boundary condition, β j j > 0 , β i j = β j i ≤ 0 , for i ≠ j. The existence of infinitely many sign-changing solutions is proved by the truncation method and by the concentration analysis on the approximating solutions, provided N > p + p 2 .
- Subjects
EQUATIONS; LAPLACIAN operator
- Publication
International Journal of Mathematics, 2018, Vol 29, Issue 2, pN.PAG
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X18500088