Commun. Math. Anal.

Volume 8, Number 3 (2010), 92 - 101

Optimal Conditions of Solvability and Unsolvability of Nonlocal Problems for Essentially Nonlinear Differential Systems

Optimal Conditions of Solvability and Unsolvability of Nonlocal Problems for Essentially Nonlinear Differential Systems

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### Abstract

Unimprovable, in a certain sense, sufficient conditions of solvability and unsolvability of nonlocal problems are found for the differential system

$\frac{dx_i}{dt} =f_i(t,x_1,\dots,x_n) \quad (i=1,\dots,n),$

where each of the functions *$**f_i:[a,b]\times R^n \to R$* $(i=1,\dots,n)$ may be superlinear or sublinear with respect to phase variables.