AUTHORS: Anita Kirichuka, Felix Sadyrbaev

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The equation x 00 = −a(x − x 3 ) (i) is considered together with the boundary conditions x 0 (0) = 0, x0 (1) = 0 (ii), x0 (0) = 0, x0 (T) = 0 (iii). The exact number of solutions for the boundary value problems (BVP) (i), (ii) and (i), (iii) is given. The problem of finding the initial values x0 = x(0) of solutions to the problem (i), (iii) is solved also.

KEYWORDS: Boundary value problem, Jacobian elliptic functions, cubic nonlinearity, phase trajectory, multiplicity of solutions

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