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• W2952649144 abstract "In this paper we consider the higher order Lioville-type equation $(-Delta)^{m} u=rho^{2m} V(x) e^{u}$ in $Omegasubseteqmathbb{R}^{2m}$ with $Vneq0$ a given smooth potential, $rhoinmathbb{R}^{+}$ a small parameter which tends to zero from above and where we prescribe the boundary conditions to be either Navier or Dirichlet. We find sufficient conditions under which, as $rho$ approaches $0$, there exists an explicit class of solutions which admit a concentration behavior with a prescribed bubble profile around some given $k$-points in $Omega$, for any given integer $k$. These are the so-called singular limits. The candidate $k$-points of concentration must be critical points of a suitable finite dimensional functional explicitly defined in terms of the potential $V$ and the higher order Green's function with respect to the imposed boundary conditions." @default.
• W2952649144 created "2019-06-27" @default.
• W2952649144 creator A5008935529 @default.
• W2952649144 date "2015-04-01" @default.
• W2952649144 modified "2023-09-27" @default.
• W2952649144 title "Singular limits in higher order Lioville-type equations" @default.
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• W2952649144 hasPublicationYear "2015" @default.
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