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Zbl 0819.34019
O'Regan, Donal
Existence principles for second order nonresonant boundary value problems.
(English)
[J] J. Appl. Math. Stochastic Anal. 7, No.4, 487-507 (1994). ISSN 1048-9533; ISSN 1687-2177/e

The existence of a solution $y$ to the equation ${1 \over p(t)} (p(t) y'(t))' = f(t, y(t), p(t)y'(t))$ a.e. in $[0,1]$ which satisfies either Sturm-Liouville, or Neumann or periodic or Bohr conditions is established under the assumption that $p \in C[0,1] \cap C\sp 1(0,1)$, $p(t) > 0$ in $(0,1)$ and $pf$ is an $L\sp 1$-Carathéodory function.
[W.Šeda (Bratislava)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
34B24 Sturm-Liouville theory
34B27 Green functions

Keywords: Sturm-Liouville; Neumann; periodic and Bohr boundary value problems; nonlinear alternative

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