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Positive solutions for a class of semilinear two-point boundary value problems. (English) Zbl 0745.34017
The author investigates the existence of positive solutions of the periodic Neumann or Dirichlet problem for the semilinear equation \(u''+f(t,u)=0\), \(0\leq t\leq T\), where \(f\) is a Carathéodory function. The techniques used are based on the fixed point index of a compact cone map, and the mountain-pass lemma of the critical point theory.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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