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Murcia, Gaetano Siciliano","submitted_at":"2018-05-01T10:01:23Z","abstract_excerpt":"In this paper we consider the following Schr\\\"odinger-Poisson system in the whole $\\mathbb R^{3}$, \\begin{equation*}\n  \\left\\{\n  \\begin{array}{ll}\n  -\\Delta u+u+ \\lambda \\phi u=f(u) &\\text{ in } \\mathbb R^3,\n  -\\Delta \\phi= u^2 &\\text{ in } \\mathbb R^3,\n  \\end{array}\n  \\right. \\end{equation*} where $\\lambda>0$ and the nonlinearity $f$ is \"asymptotically cubic\" at infinity. This implies that the nonlocal term $\\phi u$ and the nonlinear term $f(u)$ are, in some sense, in a strict competition. 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Murcia, Gaetano Siciliano","submitted_at":"2018-05-01T10:01:23Z","abstract_excerpt":"In this paper we consider the following Schr\\\"odinger-Poisson system in the whole $\\mathbb R^{3}$, \\begin{equation*}\n  \\left\\{\n  \\begin{array}{ll}\n  -\\Delta u+u+ \\lambda \\phi u=f(u) &\\text{ in } \\mathbb R^3,\n  -\\Delta \\phi= u^2 &\\text{ in } \\mathbb R^3,\n  \\end{array}\n  \\right. \\end{equation*} where $\\lambda>0$ and the nonlinearity $f$ is \"asymptotically cubic\" at infinity. This implies that the nonlocal term $\\phi u$ and the nonlinear term $f(u)$ are, in some sense, in a strict competition. 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