A uniqueness result for a semilinear elliptic problem: a computer-assisted proof

DOI10.1016/j.jde.2009.06.023zbMath1179.35149OpenAlexW1968663132MaRDI QIDQ1032871

D. Roth, Michael Plum, Patrick J. McKenna, Filomena Pacella

Publication date: 5 November 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2009.06.023

zbMATH Keywords

uniquenesscomputer-assisted proofsemilinear elliptic boundary value problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (13)

Rigorous Numerical Enclosures for Positive Solutions of Lane–Emden’s Equation with Sub-Square Exponents ⋮ Existence and orbital stability/instability of standing waves with prescribed mass for the \(L^2\)-supercritical NLS in bounded domains and exterior domains ⋮ A computer assisted study of uniqueness of ground state solutions ⋮ Families of Periodic Solutions for Some Hamiltonian PDEs ⋮ Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods ⋮ Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof ⋮ A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain ⋮ Sign-definiteness of \(q\)-eigenfunctions for a super-linear \(p\)-Laplacian eigenvalue problem ⋮ A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations ⋮ Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains ⋮ A posteriori verification of the positivity of solutions to elliptic boundary value problems ⋮ Orbital stability investigations for travelling waves in a nonlinearly supported beam ⋮ Rigorous FEM for One-Dimensional Burgers Equation

Uses Software

• C-XSC 2.0
• INTLAB

Cites Work

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