Positive solutions to a fractional equation with singular nonlinearity

First, for any δ>0 and for λ> small enough, we prove the existence of solutions to (Pλ). Next, for a suitable range of values of δ, we show the existence of an unbounded connected branch of solutions to (Pλ) emanating from the trivial solution at λ=0. For a certain class of nonlinearities f, we derive a global multiplicity result that extends results proved in [2]. To establish the results, we prove new properties which are of independent interest and deal with the behavior and Hölder regularity of solutions to (Pλ).