A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem

DOI10.1007/978-3-0348-0249-9_3zbMath1253.35046arXiv1210.5893OpenAlexW1845670705MaRDI QIDQ3145991

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

Publication date: 17 December 2012

Published in: Inequalities and Applications 2010 (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.5893

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) Nonlinear elliptic equations (35J60)

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Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation ⋮ Rigorous Numerical Enclosures for Positive Solutions of Lane–Emden’s Equation with Sub-Square Exponents ⋮ Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods ⋮ A computer-assisted existence proof for Emden's equation on an unbounded L-shaped domain ⋮ 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 ⋮ Rigorous FEM for One-Dimensional Burgers Equation ⋮ Finite element approximation of invariant manifolds by the parameterization method

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