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Multiplicity results for sign changing bound state solutions of a semilinear equation

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Carmen Cortázar, Marta García-Huidobro, Pilar Herreros

Analysis of PDEs · Submitted 26 May 2015

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

The authors' main claim In this paper we give conditions on $f$ so that problem $$ \Delta u +f(u)=0,\quad x\in \mathbb{R}^N, N\ge 2, $$ has at least two radial bound state solutions with any prescribed number of zeros, and such that $u(0)$ belongs to a specific subinterval of $(0,\infty)$.

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arXiv ID1505.07132 (version 1)
Pith IDOQ64GIIM, Pith's permanent record of this paper and its review
CitationCarmen Cort\'azar, Marta Garc\'ia-Huidobro, Pilar Herreros. "Multiplicity results for sign changing bound state solutions of a semilinear equation." arXiv:1505.07132 (2015). https://pith.science/paper/OQ64GIIM
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The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,423 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.75 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we give conditions on $f$ so that problem $$ \Delta u +f(u)=0,\quad x\in \mathbb{R}^N, N\ge 2, $$ has at least two radial bound state solutions with any prescribed number of zeros, and such that $u(0)$ belongs to a specific subinterval of $(0,\infty)$. This property will allow us to give conditions on $f$ so that this problem has at least any given number of radial solutions having a prescribed number of zeros.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we give conditions on $f$ so that problem $$ \Delta u +f(u)=0,\quad x\in \mathbb{R}^N, N\ge 2, $$ has at least two radial bound state solutions with any prescribed number of zeros, and such that $u(0)$ belongs to a specific subinterval of $(0,\infty)$. result 0.63 0.93 0.85 asserted 1.00
s1 This property will allow us to give conditions on $f$ so that this problem has at least any given number of radial solutions having a prescribed number of zeros. interpretation 0.86 0.60 0.30 asserted 0.69

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

The paper
Original abstract

In this paper we give conditions on $f$ so that problem $$ \Delta u +f(u)=0,\quad x\in \mathbb{R}^N, N\ge 2, $$ has at least two radial bound state solutions with any prescribed number of zeros, and such that $u(0)$ belongs to a specific subinterval of $(0,\infty)$. This property will allow us to give conditions on $f$ so that this problem has at least any given number of radial solutions having a prescribed number of zeros.

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