Positive Solutions for Singular BVPs with Sign Changing and Derivative Depending Nonlinearity on the Positive Half-Line

This work is devoted to the existence of positive, vanishing nontrivial solutions for singular boundary value problems on the half-line. The nonlinearity, which encompasses some physical laws, depends on the solution and its derivative, may exhibit a singularity at the origin in its second argument and is further allowed to change sign. Existence results are proved using two different methods: the upper and lower solutions technique and the fixed point index on cones of weighted Banach spaces. The singularity is treated by means of regularization, approximation and compactness arguments. The problem originates from chemistry and biology.