Elliptic equations with critical exponent on spherical caps of \(S^{3}\)

DOI10.1007/BF02790278zbMath1151.35035OpenAlexW2021999308MaRDI QIDQ2479606

Lambertus A. Peletier, Haim Brezis

Publication date: 1 April 2008

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02790278

zbMATH Keywords

critical exponentelliptic equationspherical caps of \(S^3\)

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Critical exponents in context of PDEs (35B33) Boundary value problems on manifolds (58J32)

Related Items (26)

The Brezis-Nirenberg problem for the Laplacian with a singular drift in \(\mathbb{R}^n\) and \(\mathbb{S}^n\) ⋮ Multi-peak solutions for super-critical elliptic problems in domains with small holes ⋮ The Emden-Fowler equation on a spherical cap of \(\mathbb{S}^n\) ⋮ Bifurcation analysis of a singular nonlinear Sturm–Liouville equation ⋮ Uniqueness of positive radial solutions of the Brezis-Nirenberg problem on thin annular domains on \(\mathbb{S}^n\) and symmetry breaking bifurcations ⋮ New type of positive bubble solutions for a critical Schrödinger equation ⋮ The prescribed scalar curvature problem for polyharmonic operator ⋮ Symmetry breaking bifurcation from solutions concentrating on the equator of \(\mathbb S^N\) ⋮ Constructing solutions for the prescribed scalar curvature problem via local Pohozaev identities ⋮ Isolated boundary singularities of semilinear elliptic equations ⋮ Multi-piece of bubble solutions for a nonlinear critical elliptic equation ⋮ Bifurcating Solutions of a Nonlinear Elliptic Neumann Problem on Large Spherical Caps ⋮ Existence and properties of bubbling solutions for a critical nonlinear elliptic equation ⋮ Multiple Clustered Layer Solutions for Semilinear Elliptic Problems onSⁿ ⋮ Construction of solutions via local Pohozaev identities ⋮ A generalized Pohožaev identity and uniqueness of positive radial solutions of \(\Delta u+g(r)u+h(r)u^p=0\) ⋮ Doubling the equatorial for the prescribed scalar curvature problem on \(\mathbb{S}^N\) ⋮ On some conjectures proposed by Haïm Brezis. ⋮ Infinitely many solutions for the Schrödinger equations in \(\mathbb R^N\) with critical growth ⋮ Elliptic equations with critical exponent on a torus invariant region of 𝕊3 ⋮ Uniqueness for the Brezis-Nirenberg problem on compact Einstein manifolds ⋮ Non-radial clustered spike solutions for semilinear elliptic problems on \(S^N\) ⋮ On some nonlinear equations with critical exponents ⋮ Elliptic equations in dimension three: A conjecture of H. Brezis ⋮ Bubble solutions for an elliptic problem with critical growth in exterior domain ⋮ Elliptic equations with critical Sobolev exponents in dimension 3

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