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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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2002
The celebrated Cauchy singular integral operator on a Jordan curve, or more precisely, its 1-periodic counterpart is perhaps the most important brick in the theory of periodic integral and pseudodifferential operators. In this chapter, we first treat the Cauchy singular operators in the Holder spaces C α (Γ) and after that we extend the results to L 2 ...
Jukka Saranen, Gennadi Vainikko
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The celebrated Cauchy singular integral operator on a Jordan curve, or more precisely, its 1-periodic counterpart is perhaps the most important brick in the theory of periodic integral and pseudodifferential operators. In this chapter, we first treat the Cauchy singular operators in the Holder spaces C α (Γ) and after that we extend the results to L 2 ...
Jukka Saranen, Gennadi Vainikko
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1989
In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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In this chapter we will consider one-dimensional singular integral equations involving Cauchy principal values that arise from boundary value problems for holomorphic functions. The investigations of these integral equations with Cauchy kernels by Gakhov, Muskhelishvili, Vekua, and others have had a great impact on the further development of the ...
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1995
Let the function f be defined on I=[a,b] and, possibly, be singular at an interior point c∈(a,b). Recall that the improper integral was defined by $$\int\limits_{a}^{b} {f\left( x \right)} dx: = \mathop{{\lim }}\limits_{{\mathop{{{{\varepsilon }_{1}} \to 0}}\limits_{{{{\varepsilon }_{1}} > 0}} }} \int\limits_{a}^{{c - {{\varepsilon }_{1}}}} {f\left(
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Let the function f be defined on I=[a,b] and, possibly, be singular at an interior point c∈(a,b). Recall that the improper integral was defined by $$\int\limits_{a}^{b} {f\left( x \right)} dx: = \mathop{{\lim }}\limits_{{\mathop{{{{\varepsilon }_{1}} \to 0}}\limits_{{{{\varepsilon }_{1}} > 0}} }} \int\limits_{a}^{{c - {{\varepsilon }_{1}}}} {f\left(
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2012
The theory introduced in previous chapters, especially the Fredholm Theory, was presented under the restrictive assumptions that the kernel was continuous on its domain of definition and that the interval of integration was finite. There is no guarantee that those results or similar ones will hold if the kernel has an infinite discontinuity or if the ...
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The theory introduced in previous chapters, especially the Fredholm Theory, was presented under the restrictive assumptions that the kernel was continuous on its domain of definition and that the interval of integration was finite. There is no guarantee that those results or similar ones will hold if the kernel has an infinite discontinuity or if the ...
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A Method for Studying Singular Integral Equations
Siberian Mathematical Journal, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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