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A Note on a Singular Integral Equation Arising in a Problem in Communications
Author(s) -
Agarwal R.P.,
O'Regan D.
Publication year - 2001
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/1521-4001(200107)81:7<499::aid-zamm499>3.0.co;2-2
Subject(s) - integral equation , mathematics , mathematical analysis , singular integral , calculus (dental) , singular solution , medicine , dentistry
Positive solutions are established for the singular integral equation $y(t) = f(t) + {\int ^1 _0} k(t, s) \left [{ {{1} \over {[y(s)] ^{\alpha}}} + h(y(s))} \right ] ds, t \in [0, 1]$ and α > 0 fixed. The case f ≡ h ≡ 0, α =1 arises in communication theory.