Positive solutions for a class of implicit and discontinuous second order functional differential equations with singularities.
The authors deal with existence and approximation of a positive solution for the following implicit second-order problem \[ Lu(x)=q(x,u,Lu)\quad \text{a.e. }x\in [0,\alpha], \qquad u(0)=0,~k(u(0),u)u'(0)=0, \] with \[ Lu(x):=\frac{1}{u(x)}\left[(k(u(x),u)u'(x))'-f(x,u(x),u)u'(x)\right]-g(x,u(x),u). \] This problem shows singularities, discontinuous, functional dependence and arises in real phenomena in connection with diffusion.
scientific article; zbMATH DE number 1977931