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- Title
Boundary Value Problems for the Perturbed Dirac Equation.
- Authors
Yuan, Hongfen; Shi, Guohong; Hu, Xiushen
- Abstract
The perturbed Dirac operators yield a factorization for the well-known Helmholtz equation. In this paper, using the fundamental solution for the perturbed Dirac operator, we define Cauchy-type integral operators (singular integral operators with a Cauchy kernel). With the help of these operators, we investigate generalized Riemann and Dirichlet problems for the perturbed Dirac equation which is a higher-dimensional generalization of a Vekua-type equation. Furthermore, applying the generalized Cauchy-type integral operator F ˜ λ , we construct the Mann iterative sequence and prove that the iterative sequence strongly converges to the fixed point of operator F ˜ λ.
- Subjects
BOUNDARY value problems; DIRAC equation; CAUCHY integrals; RIEMANN-Hilbert problems; GENERALIZED integrals; INTEGRAL operators; SINGULAR integrals
- Publication
Axioms (2075-1680), 2024, Vol 13, Issue 4, p238
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms13040238