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The solution of the two-point boundary value problem for a nonlinear differential equation of the third order. (English) Zbl 0627.34022
For the problem \(x\prime''+x=0\), \(x^{(i)}(0)-x^{(i)}(2\pi /\sqrt{3})=0\), \(i=0,1,2\) Green’s function G(t,s) is constructed. It is shown that \(G(t,s)>0\) on its domain. With its help the existence of a periodic solution to the nonlinear equation \(x\prime''+F(t,x,x',x'')+x=e(t)\) is established.
MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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References:
[1] COLLATZ L.: Funkcionální analýza a numerická matematika. Praha, 1970.
[2] KOLMOGOROV A. N., FOMIN S. V.: Základy teorie funkcí a funkcionální analýzy. Praha, 1975.
[3] REKTORYS K. a kol.: Přehled užité matematiky. Praha, 1963. · Zbl 0175.15801
[4] ŠEDA V.: An Application of Green’s Function in the Differential Equations. Proceedings of Equadiff II, Acta Fac. Rerum Natur. Univ. Comenian. Math. 17, 1967, 221–235. · Zbl 0186.14902
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