Results 241 to 250 of about 105,807 (283)

Nonlinear singular integral equations in lebesgue spaces

Journal of Mathematical Sciences, 2011
Using the theory of monotone operators, existence and uniqueness for singular integral equations of the type \[ \lambda_1a(x)u(x)+{\lambda_2\over\pi}\int_a^b {\bigl(w(x)+w(s)\bigr){\mathcal K}(x,s)u(s)\over s-x}ds+ \lambda_3F\bigl(x,u(x)\bigr)=f(x), \] of singular Hammerstein integral equations of the type \[ u(x)+{\lambda\over\pi}\int_a^b {\bigl(w(x ...
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On a Class of Nonlinear Singular Integral Equations

ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1985
The present communication is a continuation of a previous paper by the author [ibid. 63, 249-259 (1983; Zbl 0525.45004)]. In that paper, the author has applied methods of monotone operator theory to some classes of nonlinear singular integral and integro-differential equations of Cauchy type.
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The Smoothness of Solutions to Nonlinear Weakly Singular Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1994
The differential properties of a solution of a nonlinear multidimensional weakly singular integral equation of the Uryson type on an open bounded set G \in \mathbb R^n are examined.
Pedas, A., Vainikko, G.
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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
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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.
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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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Successive approximations method for solving 2D nonlinear singular Fredholm integral equations

2023
Summary: In the present paper, we propose a numerical method based on the combination of the fixed point method and quadrature formula for solving two-dimensional nonlinear Fredholm integral equations of the second kind (2DNFIEs). Using uniform and partial modulus of continuity, the error estimation is given.
Doostdar, Mohammad Reza, Kazemi, Manochehr, Ghorbani, Morteza   +2 more
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Nonlinear Singular Integral Equations

2011
Abel’s integral equation, linear or nonlinear, occurs in many branches of scientific fields [1], such as microscopy, seismology, radio astronomy, electron emission, atomic scattering, radar ranging, plasma diagnostics, X-ray radiography, and optical fiber evaluation. Linear Abel’s integral equation is the earliest example of an integral equation.
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Quadrature solution methods for nonlinear singular integral equations

Russian Mathematics, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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.
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