caa a22 4500 606193812 CHVBK 20210128100911.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0335-0 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0335-0 Morlando Fabrizio Università degli Studi Roma Tre, Largo S. Leonardo Murialdo 1, 00146, Rome, Italy aut Singular limits in higher order Liouville-type equations [Elektronische Daten] [Fabrizio Morlando] In this paper we consider the following higher order boundary value problem $$\left\{ \begin{array}{l@{\quad}l} (-\Delta)^{m} u=\rho^{2m} V(x) e^{u}& \mbox{in} \ \Omega\\ B_{j}u=0, |j|\leq m-1& \mbox{on} \ \partial\Omega,\ \end{array} \right.$$ ( - Δ ) m u = ρ 2 m V ( x ) e u in Ω B j u = 0 , | j | ≤ m - 1 on ∂ Ω , where $${\Omega}$$ Ω is a smooth bounded domain in $${\mathbb{R}^{2m}}$$ R 2 m , $${m\in\mathbb{N}}$$ m ∈ N , $${V(x)\neq0}$$ V ( x ) ≠ 0 is a smooth function positive somewhere in $${\Omega}$$ Ω and $${\rho}$$ ρ is a positive small parameter. Here, the operator B j stands for either Navier or Dirichlet boundary conditions. We find sufficient conditions under which, as $${\rho}$$ ρ 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 $${\Omega}$$ Ω , for any given integer k. These are the so-called singular limits. Springer Basel, 2015 Higher order nonlinear elliptic equation nationallicence Concentrating solution nationallicence Lyapunov-Schmidt reduction nationallicence Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1545-1571 1021-9722 22:6<1545 2015 22 30 https://doi.org/10.1007/s00030-015-0335-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0335-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Morlando Fabrizio Università degli Studi Roma Tre, Largo S. Leonardo Murialdo 1, 00146, Rome, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1545-1571 1021-9722 22:6<1545 2015 22 30