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Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals

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Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu

Analysis of PDEs · Submitted 7 Apr 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity.

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arXiv ID1404.1724 (version 1)
Pith IDPA5S36UG, Pith's permanent record of this paper and its review
CitationArghir Zarnescu, Luc Nguyen, Radu Ignat, Valeriy Slastikov. "Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals." arXiv:1404.1724 (2014). https://pith.science/paper/PA5S36UG
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,580 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; .

We study a singular nonlinear ordinary differential equation on intervals $[0,R)$ with $R\le +\infty$, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study a singular nonlinear ordinary differential equation on intervals $[0,R)$ with $R\le +\infty$, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. background 0.58 0.79 0.04 asserted 0.97
s1 We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. result 0.97 0.97 0.63 asserted 1.00
s2 Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. result 0.95 0.96 0.19 asserted 1.00
s3 Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability. result 0.76 0.96 0.11 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

We study a singular nonlinear ordinary differential equation on intervals $[0,R)$ with $R\le +\infty$, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability.

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