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Keywords:
integral-recurrence equation; first order differential recurrence equations; discrete-continuous convolution; combinatorial discrete-continuous convolution; auto-convolution; Laplace transform
integral-recurrence equation; first order differential recurrence equations; discrete-continuous convolution; combinatorial discrete-continuous convolution; auto-convolution; Laplace transform
Summary:
Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.
References:
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[3] Cîrnu, M.: Initial–value problems for first–order differential recurrence equations with auto–convolution. Electron. J. Differential Equations 2 (2011), 1–13. MR 2764319 | Zbl 1258.34023
[4] Flaisher, N. M.: A certain differential recurrence equation. Arch. Math. (Brno) 4 (4) (1968), 237–239, (Russian). MR 0262631
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