Existence of positive solutions for \(p\)-Laplacian singular boundary value problems
The authors consider the following \(p\)-Laplacian singular boundary value problem \[ (\phi_p(u'))'+ q(t) f(t,u,u')= 0,\qquad 0< t< 1,\qquad u(0)= u'(1)= 0, \] where \(\phi_p(u)=|u|^{p- 2}u\), \(p> 1\), and the function \(f\) may be singular at (i) \(u'=0\) but not \(u= 0\), (ii) \(u= 0\) and \(u'= 0\). By using Leray-Schauder degree theory, positive solutions are established.
scientific article; zbMATH DE number 1890870