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Zbl 1088.34012
Li, Fuyi; Liang, Zhanping; Zhang, Qi
Existence of solutions to a class of nonlinear second order two-point boundary value problems.
(English)
[J] J. Math. Anal. Appl. 312, No. 1, 357-373 (2005). ISSN 0022-247X

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.
[Sotiris K. Ntouyas (Ioannina)]
MSC 2000:
*34B15 Nonlinear boundary value problems of ODE
47H07 Positive operators on ordered topological linear spaces
47J30 Variational methods

Keywords: two-point boundary value problems; strongly monotone operator principle; critical point theory; P.S. condition; mountain pass lemma

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