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Solvability of nonlocal boundary value problems for ordinary differential equations of higher order. (English) Zbl 1052.34024

Applying the coincidence degree arguments due to J. Mawhin, the authors prove the existence of solutions of the equation \[ x^{(n)}= f(t, x,x',\dots, x^{(n-1)})+ e(t),\quad t\in (0,1), \] satisfying the nonlocal boundary conditions \[ x^{(i)}(0)= 0,\quad i= 1,\dots, n-1,\quad x(1)= \int^1_0 x(s)\,dg(s). \] Sufficient conditions are obtained in terms of \(e\), \(f\), \(g\). In one of two main theorems the degree of the representing operator can be greater than 1.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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