Results 261 to 270 of about 3,311 (299)

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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Integrability and singularity structure of coupled nonlinear Schrödinger equations

Chaos, Solitons & Fractals, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Radhakrishnan, R., Sahadevan, R., Lakshmanan, M.   +2 more
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On a Class of Nonlinear Singular Integral Equations with Carleman Shift in Generalized Holder Spaces

Mathematical and Computational Applications, 2004
The paper concerns with the investigation of a class of nonlinear singular integral equations with Carlernan shift. Existence results are given by application of Schauder\u27s fixed-point theorem to this type of equations in generalized Holder ...
S. Amer, S. Dardery
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Numerical analysis of Newton projection methods for nonlinear singular integral equations

Journal of Computational and Applied Mathematics, 1994
Numerical methods of Newton iteration type for the solution of two classes of nonlinear Cauchy singular integral equations are studied. The existence of appropriate initial approximations, the solvability of the linearized discrete equations, and the ...
Peter Junghanns
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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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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 THE METHOD OF SOLUTION FOR A KIND OF NONLINEAR SINGULAR INTEGRAL EQUATION

Acta Mathematica Scientia, 2004
The author considers the nonlinear singular integral equation \[ \phi(t)^{2}+\frac{2b}{\pi i}\int_{L}\frac{\phi(\tau)}{\tau-t}d\tau=f(t), \quad t\in L, \] where \(L\) is a closed countour in the complex plane, \(b\not=0\) is a constant and \(f(t)\) is a polynomial. Certain special cases of the above equation are considered.
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The method of Kantorovich majorants to nonlinear singular integral equation with shift

Applied Mathematics and Computation, 2009
For a simple closed contour \(L\) in the complex plane and a shift function \(\alpha\) satisfying \(\alpha(\alpha(t))=t\) the nonlinear singular integral equation \[ \begin{multlined} a(t)u(t)+b(t)u(\alpha(t))+ {c(t)\over\pi i}\int_L{u(\tau)\over\tau-t}\,d\tau + {d(t)\over\pi i}\int_L{u(\tau)\over\tau-\alpha(t)}\,d\tau\\ - {1\over\pi i}\int_L\Bigl ...
S. M. Amer, S. Dardery
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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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A Collocation Method for a Class of Nonlinear Singular Integral Equations with a Carleman Shift

Mathematical and Computational Applications, 2012
The paper is concerned with the applicability of the collocation method to a class of nonlinear singular integral equations with a Carleman shift preserving orientation on simple closed smooth Jordan curve in the generalized Holder space Hφ(L)
Mohamed Allan
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