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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 $f: [0,1]\times {\Bbb R}\to {\Bbb R}$ 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 ODE 47H07 Monotone and positive operators on ordered topological linear spaces 47J30 Variational methods (nonlinear operator equations)
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References:
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