The role of the scalar curvature in a nonlinear elliptic problem on Riemannian manifolds
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Publication:1006418
DOI10.1007/s00526-008-0183-4zbMath1161.58310OpenAlexW2006934881WikidataQ115387626 ScholiaQ115387626MaRDI QIDQ1006418
Angela Pistoia, Anna Maria Micheletti
Publication date: 24 March 2009
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-008-0183-4
Variational principles in infinite-dimensional spaces (58E30) Elliptic equations on manifolds, general theory (58J05)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the boundary spike layer solutions to a singularly perturbed Neumann problem
- Multiplicity of solutions of a zero mass nonlinear equation on a Riemannian manifold
- Large amplitude stationary solutions to a chemotaxis system
- Uniqueness of positive solutions of \(\Delta u-u+u^ p=0\) in \(R^ n\)
- Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures
- On the interior spike layer solutions to a singularly perturbed Neumann problem
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory
- Multipeak solutions for a semilinear Neumann problem
- Multiple interior peak solutions for some singularly perturbed Neumann problems.
- Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
- Scalar curvature on \(S^ n\) and first spherical harmonics
- Multiple boundary peak solutions for some singularly perturbed Neumann problems
- On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds
- Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold
- Singularly perturbed nonlinear elliptic problems on manifolds
- Blow-up phenomena for the Yamabe equation
- On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain
- On the shape of least‐energy solutions to a semilinear Neumann problem
- On a singularly perturbed equation with neumann boundary condition
- On the Role of Mean Curvature in Some Singularly Perturbed Neumann Problems
- On the effect of critical points of distance function in superlinear elliptic problems