Multiple solutions for a superlinear and periodic elliptic system on $${\mathbb{R}^N}$$ |
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Authors: | Fukun Zhao Leiga Zhao Yanheng Ding |
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Institution: | 1.Department of Mathematics,Yunnan Normal University,Kunming,People’s Republic of China;2.Department of Mathematics,Beijing University of Chemical technology,Beijing,People’s Republic of China;3.Institute of Mathematics,AMSS, CAS,Beijing,People’s Republic of China |
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Abstract: | This paper is concerned with the following periodic Hamiltonian elliptic system $$\left \{\begin{array}{l}-\Delta u+V(x)u=g(x,v)\, {\rm in }\,\mathbb{R}^N,\\-\Delta v+V(x)v=f(x,u)\, {\rm in }\, \mathbb{R}^N,\\ u(x)\to 0\, {\rm and}\,v(x)\to0\, {\rm as }\,|x|\to\infty,\end{array}\right.$$ where the potential V is periodic and 0 lies in a gap of the spectrum of ?Δ + V, f( x, t) and g( x, t) depend periodically on x and are superlinear but subcritical in t at infinity. By establishing a variational setting, existence of a ground state solution and multiple solution for odd f and g are obtained. |
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