On a two-point boundary value problem of Duffing type equation with Dirichlet conditions. (English) Zbl 0937.34017
The paper is devoted to the study of the following boundary value problem
\[
u''+cu+g(t,u)=e(t),\qquad u(0)=u(\pi)=0.
\]
The authors obtain an existence and uniqueness result under suitable conditions on e and g. Their arguments are based on the application of a min-max theorem for \(C^{2}\) functionals.
Reviewer: Abdelkader Boucherif (Dhahran)
MSC:
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 49J99 | Existence theories in calculus of variations and optimal control |
| 49R50 | Variational methods for eigenvalues of operators (MSC2000) |
| 34H05 | Control problems involving ordinary differential equations |
References:
| [1] | Shen Zuhe, On the periodic solution to the Newtonian equation of motion. Nonlinear Analysis, 1989, 13 (2): 145–150. · Zbl 0681.70004 · doi:10.1016/0362-546X(89)90040-0 |
| [2] | Manasevich, R. E., A Min Max theorem, J. Math. Anal. Appl., 1982, 90: 64–71. · Zbl 0497.49023 · doi:10.1016/0022-247X(82)90044-0 |
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