Đại học Duy Tân
Ban Khoa học Công nghệ
Cung The Anh, Bùi Kim My (2017). Existence and non-existence of solutions to a Hamiltonian strongly degenerate elliptic system, In Press. (ISI, IF = 2.844)
Ngày đăng: 18/11/2018
Abstract
We study the non-existence and existence of infinitely many solutions to the semilinear degenerate elliptic system
⎧⎩⎨−Δλu=|v|p−1v−Δλv=|u|q−1uu=v=0in Ω,in Ω,on ∂Ω,
in a bounded domain Ω⊂RN with smooth boundary ∂Ω. Here p,q>1, and Δλ is the strongly degenerate operator of the form
Δλu=∑j=1N∂∂xj(λ2j(x)∂u∂xj),
where λ(x)=(λ1(x),…,λN(x)) satisfies certain conditions.
Keywords: Existence; non-existence; Pohozaev-type identity; variational method; hyperbola critical; strongly degenerate; Hamiltonian system
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