Nonexistence of solutions of the $p$-adic strings

We discuss mathematical aspects of the nonexistence of continuous (nontrivial) solutions of boundary value problems for equations of $p$-adic closed and open strings in the one-dimensional case. We find that the number of sign changes of the solution $\psi(t)$ is not equal to the order of zeros of the function $\psi^n(t)$ and that nonnegative (nonpositive) solutions do not exist. In the case of even $n$, if a solution $\psi$ exists, then the orders of zeros of the function $\psi^n$ and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form $2(2r+1)$, $r\ge0$.