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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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