Results 231 to 240 of about 2,616 (263)

Non‐linear singular integral equations on a finite interval

Mathematical Methods in the Applied Sciences, 2001
AbstractA class of nonlinear singular integral equations of Cauchy type on a finite interval is transformed to an equivalent class of (discontinuous) boundary value problems for holomorphic functions in the complex unit disk. Using recent results on the solvability of explicit Riemann–Hilbert problems, we prove the existence of solutions to the ...
Junghanns, P., Semmler, G., Weber, U., Wegert, E.   +3 more
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System of nonlinear Volterra’s integral equations with polar kernel and singularities

Nonlinear Analysis: Theory, Methods & Applications, 2007
Using one special Colombeau algebra and the method of regularization of fractional derivatives with a delta sequence, the author proves the existence and the uniqueness of the solution of a system of nonlinear Volterra integral equations with polar kernel.
openaire   +2 more sources

Monotonicity Methods for Nonlinear Singular Integral and Integro-Differential Equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1983
AbstractApplying methods of monotone operator theory existence theorems are proved for some classes of nonlinear singular integral and integro differential equations of Cauchy's type. In particular there are admitted more general nonlinearities in the considered integral equations than in the existing literature.
openaire   +1 more source

New methods for solving of nonlinear weakly singular integral equations

Kybernetes, 2006
PurposeAims to present a boundary integral equation method for solving Laplace's equation Δu=0 with nonlinear boundary conditions.Design/methodology/approachThe nonlinear boundary value problem is reformulated as a nonlinear boundary integral equation, with u on the boundary as the solution being sought.
Khosrow Maleknejad, Hamid Mesgrani
openaire   +2 more sources

Newton–Kantorovich approximations to nonlinear singular integral equation with shift

Applied Mathematics and Computation, 2011
The paper is concerned with the applicability of some new conditions for the convergence of Newton-Kantorovich approximations to solution of nonlinear singular integral equations of Uryson type with shift. The results are illustrated in generalized Holder space.
openaire   +1 more source

Numerical methods for nonlinear singular Volterra integral equations

AIP Conference Proceedings, 2012
This work is concerned with the numerical solution of two related nonlinear singular Volterra integral equations which arise in connection with a heat transfer problem. We consider product integration and collocation methods for both equations and several numerical results are presented illustrating the performance of these methods.
Teresa Diogo, Magda Rebelo
openaire   +1 more source

On the theory of nonlinear singular integral equations of Cauchy type

Mathematical Methods in the Applied Sciences, 1985
AbstractThe paper concerns the investigation of two classes of nonlinear singular integral equations with Cauchy kernel important in the applications. There are given uniqueness and existence theorems, the last by a novel application of Schauder's fixed point theorem to this type of equations.
L. v. Wolfersdorf, E. Meister
openaire   +2 more sources

Some Classes of Nonlinear Mixed Volterra and Singular Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1992
Existence theorems for some classes of nonlinear mixed Volterra and singular integral or integro-differential equations are proved applying methods of monotone operator theory and Schauder’s fixed point theorem, respectively. Moreover, uniqueness theorems for the solution are given.
openaire   +1 more source

On the existence and uniqueness of the solution of a nonlinear singular integral equation

AIP Conference Proceedings, 2017
In this paper, the existence and uniqueness of the solution of a nonlinear singular integral equation, which has broad applications in the theory of elementary particles and scattering, have been investigated in Holder space. An iteration method is proposed for the approximate solution of this nonlinear singular integral equation.
Nizami Mustafa, Veysel Nezir, Mesut Kara
openaire   +1 more source

On Approximate Solutions of Linear and Nonlinear Singular Integral Equations

2019
Singular integral equation theory has broad applications to theoretical and practical investigations in mathematics, mathematical physics, hydrodynamic and elasticity theory. This fact motivated many researchers to work on this field and their studies have showed that finding approximate solutions of linear and nonlinear singular integral equations in ...
Nizami Mustafa, Veysel Nezir
openaire   +1 more source