Ukpera, Awar Simon Asymptotic conditions for solving non-symmetric problems of third order nonlinear differential systems. (English) Zbl 1176.34022 Electron. J. Differ. Equ. 2008, Paper No. 154, 15 p. (2008). The author establishes new solvability criteria for the forced third-order nonlinear system\[ X'''+AX''+BX'+sH(t,X)=P(t),\quad t\in [0,T], \]subject to the periodic boundary conditions \[ X(0)-X(T)=X'(0)-X'(T)=X''(0)-X''(T)=0, \]where \(X=(x_i)_{1\leq i\leq n}:[0,T]\to \mathbb{R}^n\), \(A\) and \(B\) are constant real \(n\times n\) matrices, \(H=(h_i(t,X))_{1\leq i\leq n}:[0,T]\times \mathbb{R}^n\to \mathbb{R}^n\) and \(P=(p_i)_{1\leq i\leq n}:[0,T]\to \mathbb{R}^n\) are \(n\)-vectors, which are \(T\)-periodic in \(t\). Furthermore, \(H\) satisfies the Caratheodory conditions, and \(s\in\{-1,1\}\). The main tool is Mawhin’s continuation theorem. Reviewer: Minghe Pei (Jilin) Cited in 1 Document MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34C25 Periodic solutions to ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:asymptotic conditions; third order nonlinear differential systems; non-symmetric asymptotic conditions; third order nonlinear differential systems; non-symmetric problems; sharp and nonuniform nonresonance PDFBibTeX XMLCite \textit{A. S. Ukpera}, Electron. J. Differ. Equ. 2008, Paper No. 154, 15 p. (2008; Zbl 1176.34022) Full Text: EuDML EMIS