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Boundary value problems for hypergenic function vectors.

Guiling Zhang1, Chong Li1, Yonghong Xie1

  • 1College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, P.R. China.

Journal of Inequalities and Applications
|July 3, 2018
PubMed
Summary
This summary is machine-generated.

This study analyzes boundary value problems for hypergenic functions in Clifford analysis. It proves the existence of solutions for nonlinear problems and the existence and uniqueness for linear problems using fixed-point theorems.

Keywords:
Clifford analysisHypergenic function vectorLinear boundary value problemNonlinear boundary value problem

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Area of Science:

  • Clifford Analysis
  • Hypergenic Functions
  • Boundary Value Problems

Background:

  • Boundary value problems are crucial in various scientific fields.
  • Hypergenic functions in Clifford analysis present unique mathematical challenges.

Purpose of the Study:

  • To investigate boundary value problems for hypergenic function vectors.
  • To establish methods for proving the existence and uniqueness of solutions.

Main Methods:

  • Analysis of hypergenic quasi-Cauchy type integrals.
  • Application of the Schauder fixed-point theorem for nonlinear problems.
  • Utilization of the compression mapping principle for linear problems.

Main Results:

  • Properties of hypergenic quasi-Cauchy type integrals are elucidated.
  • Existence of solutions for nonlinear boundary value problems is demonstrated.
  • Existence and uniqueness of solutions for linear boundary value problems are proven.

Conclusions:

  • The study provides rigorous mathematical proofs for the solvability of specific boundary value problems in Clifford analysis.
  • The employed fixed-point theorems offer a robust framework for analyzing hypergenic function systems.