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Third-order boundary-value problem with nonlinear boundary conditions. (English) Zbl 0841.34022

The number of solutions to the problem \(y'''= f(t, y, y', y'')\), \(y(0)= A\), \(y''(0)= \sigma(y'(0))\), \(y'(T)= \tau(y(T))\) is estimated from below by means of the number of zeros of the solution to the corresponding variational problem.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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[1] Sadyrbaev, F., About the number of solutions of the two point boundary value problem, Latvian math. ann., 32, 37-41, (1988), (In Russian.) · Zbl 0702.34026
[2] Greguš, M.; Švec, M.; Šeda, V., (), (In Slovak.)
[3] Greguš, M.; Gera, M., Some results in the theory of a third-order linear differential equation, Ann. Pol. math., XLII, 93-102, (1983) · Zbl 0534.34015
[4] Lizorkin, P.I., (), (In Russian.)
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