Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds

DOI10.1007/s00229-008-0225-4zbMath1159.58012OpenAlexW2137709585WikidataQ115388377 ScholiaQ115388377MaRDI QIDQ1003158

Angela Pistoia, E. Norman Dancer, Anna Maria Micheletti

Publication date: 26 February 2009

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-008-0225-4

zbMATH Keywords

singularly perturbed elliptic problemsmultipeak solution

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Elliptic equations on manifolds, general theory (58J05)

Related Items (18)

Hopf reduction and orbit concentrating solutions for a class of superlinear elliptic equations ⋮ On spike solutions for a singularly perturbed problem in a compact Riemannian manifold ⋮ Curvature effect in the spinorial Yamabe problem on product manifolds ⋮ Multipeak solutions for the Yamabe equation ⋮ On the existence of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds ⋮ Multipeak solutions for asymptotically critical elliptic equations on Riemannian manifolds ⋮ Clustered solutions for supercritical elliptic equations on Riemannian manifolds ⋮ Clustered solutions to low-order perturbations of fractional Yamabe equations ⋮ Some generic properties of non degeneracy for critical points of functionals and applications ⋮ Vector solutions for two coupled Schrödinger equations on Riemannian manifolds ⋮ A note on solutions of Yamabe-type equations on products of spheres ⋮ Nondegeneracy of critical points of the mean curvature of the boundary for Riemannian manifolds ⋮ Solutions to a singularly perturbed supercritical elliptic equation on a Riemannian manifold concentrating at a submanifold ⋮ Generic properties of critical points of the scalar curvature for a Riemannian manifold ⋮ The Gierer-Meinhardt system on a compact two-dimensional Riemannian manifold: Interaction of Gaussian curvature and Green's function ⋮ Stable spike clusters on a compact two-dimensional Riemannian manifold ⋮ Positive solutions for a singularly perturbed nonlinear elliptic problem on manifolds via Morse theory ⋮ New Type of Sign-Changing Blow-up Solutions for Scalar Curvature Type Equations

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