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Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems

Fukun Zhao, Leiga Zhao, Yanheng Ding (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the following periodic Hamiltonian elliptic system { - Δ ϕ + V ( x ) ϕ = G ψ ( x , ϕ , ψ ) in N , - Δ ψ + V ( x ) ψ = G ϕ ( x , ϕ , ψ ) in N , ϕ ( x ) 0 and ψ ( x ) 0 as | 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.


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