Results 221 to 230 of about 2,616 (263)

On a class of nonlinear singular integral equations with shift on a closed contour

Applied Mathematics and Computation, 2004
Assuming that \(L\) is a sufficiently well behaved closed contour in the complex plane, the authors investigate the nonlinear Cauchy singular integral equation \[ \phi(t) = \Omega \sum_{j=0}^{m-1} a_j(t) \int_L { G(\alpha_j(t), \tau, \phi(\tau)) \over \tau - \alpha_j(t)} d \tau\text{ for }t \in L. \] Here \(\alpha_0(t) = t\) and \(\alpha_j(t) = \alpha(\
S. M. Amer, S. Dardery
exaly   +3 more sources

Singular nonlinear integral equations of Hammerstein type

Lecture Notes in Mathematics, 1975
Felix E Browder, Browder Felix E
exaly   +2 more sources

On the Solvability of Nonlinear Singular Integral Equations

Zeitschrift für Analysis und ihre Anwendungen, 1993
Three classes of nonlinear singular integral equations of Cauchy type occuring in the treatment of certain free boundary value problems are investigated. Existence of the solution is proved under weaker conditions than in [13] using the technique which was created in [12, 13] and is based on the application of Schauder’s fixed point theorem.
Junghanns, P., Weber, U.
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +1 more source

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.
openaire   +2 more sources

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 ...
openaire   +2 more sources

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.
openaire   +1 more source

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
openaire   +1 more source

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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