Constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems

DOI10.1007/s00211-004-0544-7zbMath1058.65129OpenAlexW2027574501MaRDI QIDQ1882393

Jiří Horák

Publication date: 1 October 2004

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-004-0544-7

zbMATH Keywords

semilinear elliptic problemssteepest descent methodconstrained mountain pass algorithm

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (10)

Energy eigenfunctions of the 1D Gross-Pitaevskii equation ⋮ A mountain pass algorithm for quasilinear boundary value problem with \(p\)-Laplacian ⋮ Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions ⋮ A new approach to solving a quasilinear boundary value problem with \(p\)-Laplacian using optimization. ⋮ Non-symmetric low-index solutions for a symmetric boundary value problem ⋮ A local minimax method using virtual geometric objects. I. For finding saddles ⋮ A local minimax method using virtual geometric objects. II. For finding equality constrained saddles ⋮ Mini-max algorithm via Pohozaev manifold ⋮ Level set methods for finding critical points of mountain pass type ⋮ Orbital stability investigations for travelling waves in a nonlinearly supported beam

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A sign-changing solution for a superlinear Dirichlet problem
• A deformation lemma on a \(C^ 1\) manifold
• A mountain pass method for the numerical solution of semilinear wave equations
• Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
• Analytical and numerical results for the Fučík spectrum of the Laplacian.
• Solitary waves in nonlinear beam equations: Stability, fission and fusion
• New solutions of the Gelfand problem
• Dual variational methods in critical point theory and applications
• A high-linking algorithm for sign-changing solutions of semilinear elliptic equations
• Travelling waves in a nonlinearly suspended beam: some computational results and four open questions
• A mountain pass method for the numerical solution of semilinear elliptic problems
• A numerical investigation of sign-changing solutions to superlinear elliptic equations on symmetric domains

This page was built for publication: Constrained mountain pass algorithm for the numerical solution of semilinear elliptic problems