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Existence of solutions for right focal boundary value problems. (English) Zbl 0755.34016

The authors are concerned with solutions of right focal boundary value problems for an \(n\)-th order scalar equation (1) \(x^{(n)}=f(t,x,x',\dots,x^{(n-1)})\), \(t\in(a,b)\), under the main assumptions that \(f\) is continuous on \((a,b)\times\mathbb{R}^ n\) and solutions of initial value problems for (1) are unique and extend to \((a,b)\). The main objective is to establish “uniqueness implies existence” results for right \((m_ 1,\dots,m_ k)\) focal boundary value problems.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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