Pith. Sign in

RECORD

Positive stationary solutions for p-Laplacian problems with nonpositive perturbation

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Aleksander Cwiszewski, Mateusz Maciejewski

Analysis of PDEs · Submitted 5 Apr 2012

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

The authors' main claim The paper is devoted to the existence of positive solutions of nonlinear elliptic equations with $p$-Laplacian.

how it is stated · asserted 0.91 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1204.1295 (version 2)
Pith IDJFSGZNIW, Pith's permanent record of this paper and its review
CitationAleksander Cwiszewski, Mateusz Maciejewski. "Positive stationary solutions for p-Laplacian problems with nonpositive perturbation." arXiv:1204.1295 (2012). https://pith.science/paper/JFSGZNIW
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,668 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The paper is devoted to the existence of positive solutions of nonlinear elliptic equations with $p$-Laplacian. We provide a general topological degree that detects solutions of the problem $$ \{{array}{l} A(u)=F(u) u\in M {array}. $$ where $A:X\supset D(A)\to X^*$ is a maximal monotone operator in a Banach space $X$ and $F:M\to X^*$ is a continuous mapping defined on a closed convex cone $M\subset X$. Next, we apply this general framework to a class of partial differential equations with $p$-Laplacian under Dirichlet boundary conditions.

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 The paper is devoted to the existence of positive solutions of nonlinear elliptic equations with $p$-Laplacian. background 0.61 0.43 0.17 asserted 0.91
s1 We provide a general topological degree that detects solutions of the problem $$ \{{array}{l} A(u)=F(u) u\in M {array}. contribution 0.82 0.93 0.22 asserted 1.00
s2 $$ where $A:X\supset D(A)\to X^*$ is a maximal monotone operator in a Banach space $X$ and $F:M\to X^*$ is a continuous mapping defined on a closed convex cone $M\subset X$. method 0.56 0.36 0.05 asserted 0.77
s3 Next, we apply this general framework to a class of partial differential equations with $p$-Laplacian under Dirichlet boundary conditions. contribution 0.61 0.93 0.09 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.92 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

The paper is devoted to the existence of positive solutions of nonlinear elliptic equations with $p$-Laplacian. We provide a general topological degree that detects solutions of the problem $$ \{{array}{l} A(u)=F(u) u\in M {array}. $$ where $A:X\supset D(A)\to X^*$ is a maximal monotone operator in a Banach space $X$ and $F:M\to X^*$ is a continuous mapping defined on a closed convex cone $M\subset X$. Next, we apply this general framework to a class of partial differential equations with $p$-Laplacian under Dirichlet boundary conditions.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.