To a first approximation, zero Libertarians believe that "the free market can solve all problems." Many of us do believe that - on balance - free markets deliver better outcomes than other approaches, but that is not a claim of perfection. Other Libertarians believe that free market approaches are simply morally superior, since any non-free-market approach seems to necessitate the use of force/violence to prevent people from simply trading freely as they would in the absence of said force/violence.

And, of course, some Libertarians hold both beliefs - that free markets are the moral approach AND that the create better outcomes more often than not. But other than maybe a few n00bs who just discovered Libertarianism from a pamphlet or something, almost nobody is going around claiming that free markets fix everything.