Abstract
In this paper we consider the following elliptic system in \({\mathbb{R}^3}\)
where λ is a real parameter, \({p\in (1, 5)}\) if λ < 0 while \({p\in (3, 5)}\) if λ > 0 and K(x), a(x) are non-negative real functions defined on \({\mathbb{R}^3}\) . Assuming that \({\lim_{|x|\rightarrow+\infty}K(x)=K_{\infty} >0 }\) and \({\lim_{|x|\rightarrow+\infty}a(x)=a_{\infty} >0 }\) and satisfying suitable assumptions, but not requiring any symmetry property on them, we prove the existence of positive ground states, namely the existence of positive solutions with minimal energy.
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Communicated by V. Coti-Zelata.
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Vaira, G. Ground states for Schrödinger–Poisson type systems. Ricerche mat. 60, 263–297 (2011). https://doi.org/10.1007/s11587-011-0109-x
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DOI: https://doi.org/10.1007/s11587-011-0109-x