Boundary clustered layers near the higher critical exponents

DOI10.1016/j.jde.2013.02.015zbMath1288.35240arXiv1211.2364OpenAlexW2008596231MaRDI QIDQ390988

Angela Pistoia, Mónica Clapp, Nils Ackermann

Publication date: 9 January 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.2364

zbMATH Keywords

nonlinear elliptic boundary value problemscritical and supercritical exponentsexistence of positive and sign changing solutions

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20) Positive solutions to PDEs (35B09)

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Concentration with a single sign-changing layer at the higher critical exponents ⋮ New type of solutions to a slightly subcritical Hénon type problem on general domains ⋮ Nonexistence and multiplicity of solutions to elliptic problems with supercritical exponents ⋮ Concentration results for a singularly perturbed elliptic system with variable coefficients ⋮ Boundary towers of layers for some supercritical problems ⋮ Supercritical problems in domains with thin toroidal holes ⋮ Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold ⋮ Bubbling solutions to an anisotropic Hénon equation ⋮ Infinitely many positive solutions for a nonlinear field equation with super-critical growth ⋮ Asymptotic behavior of least energy solutions to the Lane-Emden system near the critical hyperbola ⋮ A Supercritical Elliptic Problem in a Cylindrical Shell ⋮ Bubble Concentration on Spheres for Supercritical Elliptic Problems ⋮ Positive solutions to a supercritical elliptic problem that concentrate along a thin spherical hole

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