Geodesic
Nonexistence of solutions of the $p$-adic strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 208-215 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $2(2r+1)$, $r\ge0$.
Keywords: $p$-adic string, tachyon, pseudodifferential operator. 
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V. S. Vladimirov. Nonexistence of solutions of the $p$-adic strings. Teoretičeskaâ i matematičeskaâ fizika, Tome 174 (2013) no. 2, pp. 208-215. http://geodesic.mathdoc.fr/item/TMF_2013_174_2_a1/

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