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Ordinary differential equations with nonlinear boundary conditions of antiperiodic type. (English) Zbl 1105.34007

Consider the boundary value problem \[ x'(t)=f\bigl(t,x(t)\bigr),\quad t\in[0,T],\quad 0=g\bigl(x(0),x(T)\bigr),\tag{*} \] where \(f\) and \(g\) are continuous scalar functions and \(g\) is of antiperiodic type (e.g. \(g(u,v) =u+v)\). Using the method of lower and upper solutions, the author derives sufficient conditions such that there exist monotone sequences converging quadratically to the unique solution of (*).

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34A45 Theoretical approximation of solutions to ordinary differential equations
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References:

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