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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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