Infinitely many solutions for asymptotically linear periodic hamiltonian elliptic systems
ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 1, pp. 77-91.

This paper is concerned with the following periodic hamiltonian elliptic system {-Δφ+V(x)φ=G ψ (x,φ,ψ)in N ,-Δψ+V(x)ψ=G φ (x,φ,ψ)in N ,φ(x)0andψ(x)0as|x|. Assuming the potential V is periodic and 0 lies in a gap of σ(-Δ+V), G(x,η) is periodic in x and asymptotically quadratic in η=(φ,ψ), existence and multiplicity of solutions are obtained via variational approach.

DOI: 10.1051/cocv:2008064
Classification: 35J50, 35J55
Keywords: hamiltonian elliptic system, variational methods, strongly indefinite functionals
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     title = {Infinitely many solutions for asymptotically linear periodic hamiltonian elliptic systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {77--91},
     publisher = {EDP-Sciences},
     volume = {16},
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     year = {2010},
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     zbl = {1189.35091},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/cocv:2008064/}
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Zhao, Fukun; Zhao, Leiga; Ding, Yanheng. Infinitely many solutions for asymptotically linear periodic hamiltonian elliptic systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 1, pp. 77-91. doi : 10.1051/cocv:2008064. http://archive.numdam.org/articles/10.1051/cocv:2008064/

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