Singular boundary-value problems with variable coefficients on the positive half-line

This work concerns the existence and the multiplicity of solutions for singular boundary-value problems with a variable coefficient, posed on the positive half-line. When the nonlinearity is positive but may have a space singularity at the origin, the existence of single and twin positive solutions is obtained by means of the fixed point index theory. The singularity is treated by approximating the nonlinearity, which is assumed to satisfy general growth conditions. When the nonlinearity is not necessarily positive, the Schauder fixed point theorem is combined with the method of upper and lower solutions on unbounded domains to prove existence of solutions. Our results extend those in [18] and are illustrated with examples.