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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.

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
Full Text: DOI
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