On the structure of the solutions of Volterra integral equations with degenerate kernel

Journal Article · Wed May 10 04:00:00 EDT 1995 · Journal of Mathematical Sciences

DOI:https://doi.org/10.1007/BF02367695· OSTI ID:98980

Pleshchiniskii, N B; Tagirov, R R

Expositions of the theory of linear equations frequently begin with Fredholm equations with degenerate kernel, while Volterra equations with degenerate kernel are encountered only rarely in the literature. In the present paper we study linear Volterra integral equations of the first and second kind with a degenerate kernels. Formulas are obtained that determine the structure of the solutions of the equations considered. The following assumptions are made: the (real- or complex-valued) functions a(x), b{sub j}(x), c{sub j}(x), j=1,n, and mu(x) are continuous on [alpha, beta], or else they are square-integrable. In this case, as is known, there exists a unique continous or square integrable solution v(x).

• Sponsoring Organization: USDOE
• OSTI ID: 98980
• Journal Information: Journal of Mathematical Sciences, Journal Name: Journal of Mathematical Sciences Journal Issue: 5 Vol. 74; ISSN 1072-1964; ISSN JMTSEW
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
ALGORITHMS
ANALYTICAL SOLUTION
FREDHOLM EQUATION
INTEGRAL CALCULUS
KERNELS
VOLTERRA INTEGRAL EQUATIONS