Nonexistence of positive solutions of quasilinear differential equations (Q1381795)

If \(\sup\left\{{u^{p-1}\over f_0(u)}: u\in[0, \infty)\right\}\) is sufficiently small, with \(f_0(u)= \min\{f(t, u): t\in[a, b]\}\) and \(f(t,a)> 0\), then the equation \((| u'(t)|^{p- 2}u'(t))'+ f(t, u(t))= 0\), with \(a< t< b\), \(p>1\), has no positive solution satisfying one of the boundary conditions \(u(a)= u(b)= 0\), \(u(a)= u'(b)= 0\), \(u'(a)= u(b)= 0\).