We seek multiple solutions to systems of semilinear elliptic equations of the type-ΔU(x)=∇H(x; U(x))x∈ΩU(x)=0x∈∂Ω,where Ω⊂RN (N≥1) is a bounded regular domain and U=(u1, u2):Ω→R2. For a class of potentials where the variables are strongly coupled as in the model H(x; u1, u2)=u1α1u2α2 with αi>1, we provide the existence of nine nontrivial solutions characterized by sign properties of each component. © 2000 Academic Press.
Conti, M., Merizzi, L., Terracini, S. (2000). On the existence of many solutions for a class of superlinear elliptic systems. JOURNAL OF DIFFERENTIAL EQUATIONS, 167(2), 357-387 [10.1006/jdeq.2000.3813].
On the existence of many solutions for a class of superlinear elliptic systems
TERRACINI, SUSANNA
2000
Abstract
We seek multiple solutions to systems of semilinear elliptic equations of the type-ΔU(x)=∇H(x; U(x))x∈ΩU(x)=0x∈∂Ω,where Ω⊂RN (N≥1) is a bounded regular domain and U=(u1, u2):Ω→R2. For a class of potentials where the variables are strongly coupled as in the model H(x; u1, u2)=u1α1u2α2 with αi>1, we provide the existence of nine nontrivial solutions characterized by sign properties of each component. © 2000 Academic Press.
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