Research Article
Quasilinear elliptic system with sub-natural and natural growth terms in distinct equations
https://doi.org/10.21203/rs.3.rs-3551851/v1
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In this paper, we study the following system: −∆pu = λ*a(x)uq−1 + c(x)uα−1vβ,in Ω −∆pv = µb(x)vp−1 + c(x)uαvβ−1,in Ω 0 ̸≡ u ≥ 0, 0 ̸≡ v ≥ 0 in Ω u = v = 0 on ∂Ω where Ω ⊂ RN is a smooth bounded domain, −∆pdenotes the p-Laplacian operator, 1 < q < p < N, α,β > 1, p<α+β
0, and λ,µ>0.
2020 Mathematics Subject Classification: 35J47, 35J50, 35J92.
elliptic system
variational method
critical growth
p-Laplacian
No competing interests reported.
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