Theoretical and Mathematical Physics

, Volume 174, Issue 2, pp 178–185 | Cite as

Nonexistence of solutions of the p-adic strings

  • V. S. Vladimirov


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 ψ(t) is not equal to the order of zeros of the function ψn(t) and that nonnegative (nonpositive) solutions do not exist. In the case of even n, if a solution ψ exists, then the orders of zeros of the function ψn and the order of its tangency to positive maximums (minimums) are not divisible by four and therefore have the form 2(2 r + 1), r ≥ 0.


p-adic string tachyon pseudodifferential operator 


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© Pleiades Publishing, Ltd. 2013

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  • V. S. Vladimirov

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