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Stability analysis and exploration of multiform soliton solutions for extended fractional NLS model using modified extended direct algebraic method. [PDF]
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Nystrom technique analysis of the terahertz and infrared range radar cross section of a circular dielectric cylinder with graphene strips inside. [PDF]
Philos Trans A Math Phys Eng SciKaliberda ME, Pogarsky S.
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Singularities of Solutions of Singular Integral Equations
Ukrainian Mathematical Journal, 2002This paper deals with a singular integral equation \[ Sq+Tq=f,\tag{1} \] where \(q(x)\) is an unknown function, \[ Sq(x):=aq(x)+\frac{1}{\pi }\text{v.p.} \int_{-1}^{1} \frac{q(\tau)}{\tau -x} d\tau,\;Tq(x):=\int_{-1}^{1}K(x,\tau)q(\tau) d\tau. \] It is assumed that the functions \(f\) and \(K\) smoothly depend on additional parameters.
Kapustyan, V. E., Il'man, V. M.
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Journal of Mathematical Physics, 1966
The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
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The integral equation P ∫ cK(ζ′,ζ)ζ′−ζφ(ζ′) dζ′=h(ζ)φ(ζ)+f(ζ)is shown to have simple solutions obtained by standard and elementary methods if h and K have appropriate analytic properties.
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Solving a Singular Integral Equation
Computational Mathematics and Modeling, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Solution of a Singular Integral Equation
Differential Equations, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2003
In this chapter we discuss some recent results for Fredholm and Volterra integral equations, which deal with the existence of positive (and possibly multiple) solutions of certain classes of these equations. In Section 3.2 we provide some existence results for the nonsingular Fredholm integral equations.
Ravi P. Agarwal, Donal O’Regan
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In this chapter we discuss some recent results for Fredholm and Volterra integral equations, which deal with the existence of positive (and possibly multiple) solutions of certain classes of these equations. In Section 3.2 we provide some existence results for the nonsingular Fredholm integral equations.
Ravi P. Agarwal, Donal O’Regan
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Product Integration for Singular Integrals and Singular Integral Equations
1979Integral equations with weakly singular kernels often have solutions which have derivative singularities at the end points of the range of integration. The error analysis of a product integration method for such integral equations depends on the error analysis of the product integration method applied to integrals of the form \(\int\limits_0^1 {g\left(
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On the Solvability of Nonlinear Singular Integral Equations
Zeitschrift für Analysis und ihre Anwendungen, 1993Three 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.
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SYSTEMS OF SINGULAR INTEGRAL EQUATIONS WITH A SHIFT
Mathematics of the USSR-Sbornik, 1983Let? be a?simple closed oriented Lyapunov curve and let be an -smooth diffeomorphism of? onto itself whose set of fixed points is nonempty and finite. The system of equations is considered in the space , , where is the identity operator, is a?singular integral operator with Cauchy kernel, () are polynomials of positive and negative degree in the ...
Karlovich, Yu. I., Kravchenko, V. G.
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