Uniqueness implies existence of solutions for nonlinear $(k;j)$ point boundary value problems for nth order differential equations

J. Ehme, Spelman College, Atlanta, GA, U.S.A.

E. J. Qualitative Theory of Diff. Equ., Spec. Ed. I, 2009 No. 11., pp. 1-9.

Abstract: Given appropriate growth conditions for $f$ and a uniqueness assumption on $y^{(n)}=0$ with respect to certain $(k;j)$ point boundary value problems, it is shown that uniqueness of solutions to the nonlinear differential equation
\[
y^{(n)}=f(t,y,y^{\prime },\dots ,y^{(n-1)}),
\]
subject to nonlinear $(k;j)$ boundary conditions of the form
\[
g_{ij}(y(t_{j}),\ldots ,y^{(n-1)}(t_{j}))=y_{ij},
\]
implies existence of solutions.

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