I'm reading a definition of PSPACE and say: are the decision problems solvable in polynomial space on a Deterministic Turing Machine. My question is: Why NP is in PSPACE?. I have a doubt beccause for example a SAT problem is solvable in Non-Deterministic Turing Machine and SAT $\in NP$ and not in $P$.
NP is a complexity class with constraints on time, whilst PSPACE is a complexity class with constraints on space. The difference between time and space is (in this case) simple: Space can be reused, whilst Time cannot. A Space-bounded machine can run for as long as it wants (as long as it terminates).
Therefore we can construct a PSPACE-Machine that solves SAT: The machine simply tries every solution.