I've got many problems to solve.

Literal

I [to-は] solve must problem [subject-が] many.

The relative clause 解決しなければならない modifies 問題 — '[problems that] must be solved.' Japanese relative clauses precede the noun with no linker. 多い ('many') is the predicate, taking the subject-marking が on 問題. A compact packing of obligation + relative clause + predicate.