On Solving Semilinear Singularly Perturbed Neumann Problems for Multiple Solutions
DOI10.1137/20M1383380zbMath1483.58002OpenAlexW4214737809MaRDI QIDQ5037544
Yongjun Yuan, Jian Xin Zhou, Zi-Qing Xie
Publication date: 1 March 2022
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/20m1383380
bifurcationmultiple solutionsNeumann problemsingularly perturbedlocal minimax methodcritical perturbation value
Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20) Variational problems in abstract bifurcation theory in infinite-dimensional spaces (58E07) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)
Related Items (1)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the boundary spike layer solutions to a singularly perturbed Neumann problem
- Sign changing solutions with clustered layers near the origin for singularly perturbed semilinear elliptic problems on a ball
- Large amplitude stationary solutions to a chemotaxis system
- Global bifurcation of steady-state solutions
- Multidimensional nonlinear diffusion arising in population genetics
- Locating the peaks of least-energy solutions to a semilinear Neumann problem
- On spike solutions of singularly perturbed semilinear Dirichlet problem
- Search extension method for multiple solutions of a nonlinear problem
- Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability.
- Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory
- A local minimax method using virtual geometric objects. I. For finding saddles
- Multiple clustered layer solutions for semilinear Neumann problems on a ball
- Multipeak solutions for a semilinear Neumann problem
- Multiple interior peak solutions for some singularly perturbed Neumann problems.
- On the existence of multipeaked solutions to a semilinear Neumann problem
- Multiple boundary peak solutions for some singularly perturbed Neumann problems
- A constrained string method and its numerical analysis
- On the number of nodal solutions to a singularly perturbed Neumann problem
- A Minimax Method for Finding Multiple Critical Points and Its Applications to Semilinear PDEs
- On Finding Multiple Solutions to a Singularly Perturbed Neumann Problem
- On the number of interior peak solutions for a singularly perturbed Neumann problem
- On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type
- A bifurcation theorem for critical points of variational problems
- On the shape of least‐energy solutions to a semilinear Neumann problem
- On the Modular Representation Theory of the Two-Dimensional Special Linear Group Over an Algebraically Closed Field
- On a singularly perturbed equation with neumann boundary condition
- On Multiple Mixed Interior and Boundary Peak Solutions for Some Singularly Perturbed Neumann Problems
- A Local Minimax-Newton Method for Finding Multiple Saddle Points with Symmetries
- Instability analysis of saddle points by a local minimax method
- On the Role of Mean Curvature in Some Singularly Perturbed Neumann Problems
- Convergence Results of a Local Minimax Method for Finding Multiple Critical Points
- On the role of distance function in some singular perturbation problems
- An improved search-extension method for computing multiple solutions of semilinear PDEs
This page was built for publication: On Solving Semilinear Singularly Perturbed Neumann Problems for Multiple Solutions
