Let $L:U\rightarrow V$ be a linear mapping. A linear equation is called homogeneous if it has the form $$L(u)=0,\quad u\in U.$$ A homogeneous linear problem always has a trivial solution, namely $u=0$ . The key issue in homogeneous problems is, therefore, the question of the existence of non-trivial solutions, i.e. whether or not the kernel of $L$ is trivial, or equivalently, whether or not $L$ is injective.