Suppose $f(t, x)$ is nonincreasing with respect to $x$ for all $t \geq 0$ and $x \in \mathbb{R}$. Prove that the IVP problem $$ \left\{ \begin{array}{l} x'(t)=f(t,x) \\ x(t_0)=x_0 \end{array} \right. $$ has at most one solution for $t \geq t_0$.
IVP- Has at most one solution
0
$\begingroup$
analysis
ordinary-differential-equations
fixed-point-theorems