The Dirichlet Boundary Value Problem for Real Solutions of the first Painlevé Equation on Segments on Non-Positive Semi-Axis
Joshi, N. · Kitaev, A. V.
Classical Analysis and ODEs
Mathematical Physics
Exactly Solvable and Integrable Systems
33E17;34M55;34B15
Original · EN
We develop a qualitative theory for real solutions of the equation y''=6y² -x. In this work a restriction x≤0 is assumed. An important ingredient of our theory is the introduction of several new transcendental functions of one, two, and three variables that describe different properties of the solutions. In particular, the results obtained allow us to completely analyse the Dirichlet boundary value problem y(a)=y⁰, y(b)=y₀ for a<b≤0.
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