A note on a singular integral equation arising in a problem in communications (Q2747490)
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scientific article; zbMATH DE number 1657805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on a singular integral equation arising in a problem in communications |
scientific article; zbMATH DE number 1657805 |
Statements
14 July 2002
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nonlinear problem
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positive solutions
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singular integral equations
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communications
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A note on a singular integral equation arising in a problem in communications (English)
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The authors establish the existence of positive solutions of singular integral equations of the form NEWLINE\[NEWLINEy(t)=f(t)+ \int^1_0 K(t,s) \biggl[\bigl(y(s) \bigr)^{-\alpha} +h\bigl(y(s) \bigr) \biggr]ds,\quad t\in [0,1]NEWLINE\]NEWLINE and \(\alpha>0\) fixed. The integral equation NEWLINE\[NEWLINEy(t)= \int^1_0 K(t,s) \bigl(y(s) \bigr)^{-1}ds, \quad t\in[0,1],NEWLINE\]NEWLINE arises in a problem in communications [cf. \textit{P. Nowosad}, J. Math. Anal. Appl. 14, 484-492 (1966; Zbl 0182.15102)].
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