On the location and profile of spike-layer solutions to a singularly perturbed semilinear Dirichlet problem: Intermediate solutions
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Publication:1974855
DOI10.1215/S0012-7094-98-09424-8zbMath0946.35007OpenAlexW1579246209MaRDI QIDQ1974855
Wei-Ming Ni, Izumi Takagi, Wei, Juncheng
Publication date: 27 March 2000
Published in: Duke Mathematical Journal (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1215/s0012-7094-98-09424-8
Nonlinear boundary value problems for linear elliptic equations (35J65) Singular perturbations in context of PDEs (35B25)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Uniqueness of positive solutions of semilinear equations in \(R^ n\).
- Symmetry and related properties via the maximum principle
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- On spike solutions of singularly perturbed semilinear Dirichlet problem
- Dual variational methods in critical point theory and applications
- The set of positive solutions of semilinear equations in large balls
- On the shape of least‐energy solutions to a semilinear Neumann problem
- On the location and profile of spike‐layer solutions to singularly perturbed semilinear dirichlet problems