Semi-classical states for elliptic system near saddle points of potentials
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DOI: 10.1088/1361-6544/acd045
Abstract: In this paper, we study the following Hamiltonian elliptic system −ε2Δu+u=Hv(x,u,v) in RN,−ε2Δv+v=Hu(x,u,v) in RN,u(x)→0, v(x)→0 as |x|→∞, where ɛ > 0 is a small parameter, H is a super-quadratic sub-critical Hamiltonian. Our investigation focuses on the cases that H(x,u,v)=12K(x)(u2+v2)+F(u,v) and H(x,u,v)=K(x)F(u,v) , where… read more here.
Keywords: classical states; states elliptic; saddle points; elliptic system ... See more keywords