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<p/> <p>We consider the singular nonlinear integral equation <inline-formula><graphic file="1029-242X-2006-45043-i1.gif"/></inline-formula> for all <inline-formula><graphic file="1029-242X-2006-45043-i2.gif"/></inline-formula> where <inline-formula><graphic file="1029-242X-2006-45043-i3.gif"/></inline-formula> is a given positive constant and the given function <inline-formula><graphic file="1029-242X-2006-45043-i4.gif"/></inline-formula> is continuous and <inline-formula><graphic file="1029-242X-2006-45043-i5.gif"/></inline-formula> for all <inline-formula><graphic file="1029-242X-2006-45043-i6.gif"/></inline-formula> with some constants <inline-formula><graphic file="1029-242X-2006-45043-i7.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2006-45043-i8.gif"/></inline-formula>. We prove in an elementary way that if <inline-formula><graphic file="1029-242X-2006-45043-i9.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-45043-i10.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-45043-i11.gif"/></inline-formula>, <inline-formula><graphic file="1029-242X-2006-45043-i12.gif"/></inline-formula> the above nonlinear integral equation has no positive solution. </p>