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Existence of solutions to a class of nonlinear second order two-point boundary value problems. (English) Zbl 1088.34012
Existence and multiplicity results are obtained for the following boundary value problem \[ -u''(t)=f(t,u(t)), \quad t\in [0,1],\quad u(0)=u'(1)=0, \] where \(f: [0,1]\times {\mathbb R}\to {\mathbb R}\) is continuous. By using the strongly monotone operator principle and the critical point theory, the authors establish some conditions for \(f\) which guarantee that the boundary value problem has a unique solution, at least one nonzero solution, and infinitely many solutions.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
47J30 Variational methods involving nonlinear operators
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