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Existence principles for second order nonresonant boundary value problems. (English) Zbl 0819.34019
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 $$p \in C[0,1] \cap C^ 1(0,1)$$, $$p(t) > 0$$ in $$(0,1)$$ and $$pf$$ is an $$L^ 1$$-Carathéodory function.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations 34B24 Sturm-Liouville theory 34B27 Green’s functions for ordinary differential equations
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