The Gel'fand problem on expanding tubular domains in \(\mathbb{R}^2\): existence and the Morse index of solutions
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Publication:6639547
DOI10.1007/S12220-024-01843-YMaRDI QIDQ6639547
Yasuhito Miyamoto, Marius Ghergu
Publication date: 15 November 2024
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Resonance in context of PDEs (35B34) Semilinear elliptic equations (35J61) Elliptic equations and elliptic systems (35Jxx)
Cites Work
- Solutions of semilinear elliptic equations in tubes
- Morse indices and symmetry breaking for the Gelfand equation in expanding annuli
- Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus
- Asymptotically radial solutions in expanding annular domains
- Transition layer for the heterogeneous Allen-Cahn equation
- Multidimensional boundary layers for a singularly perturbed Neumann problem
- Asymptotic behavior of positive solutions to semilinear elliptic equations on expanding annuli
- Multi-bump positive solutions for a nonlinear elliptic problem in expanding tubular domains
- Symmetry breaking of an elliptic equation in expanding annuli
- Resonance and Interior Layers in an Inhomogeneous Phase Transition Model
- MULTIBUMP SOLUTIONS FOR AN ELLIPTIC PROBLEM IN EXPANDING DOMAINS
- Exact eigenvalues and eigenfunctions for a one-dimensional Gel’fand problem
- Boundary concentration phenomena for a singularly perturbed elliptic problem
- Solutions to the nonlinear Schrödinger equation carrying momentum along a curve
- Asymptotic formula for the Morse index of radial solutions on expanding annuli: Allen-Cahn equation and scalar filed equation
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