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symmetric operator; Green function; generalized Banach space; Lipschitz condition; eigenvalue
Existence and uniqueness of the solution to a fourth order nonlinear vector periodic boundary value problem is proved by using the estimates for derivatives of the Green function for the corresponding homogenous scalar problem
[1] Greguš, M., Švec, M., Šeda, V.: Obyčajné diferenciálne rovnice. Alfa, 1985.
[2] Šeda, V.: On a vector multipoint boundary value problem. Archivum Mathematicum Brno 22 (1986), no. 2, 75–92. MR 0868122
[3] Zajacová, Ĺ.: The solution of the two-point boundary value problem for a nonlinear differential equation of the third order. Math. Slovaca 36 (1986), no. 4, 345–357. MR 0871775
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