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Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian
| 1. | College of Mathematics, Jilin University, Changchun 130012 |
| 2. | Department of Mathematics, Jilin University, Changchun 130023 |
Minimize $\quad \int_a^bL(x,u(x),u'(x),u''(x))dx,\quad u\in\Omega$
with a second-order Lagrangian is considered. In absence of any smoothness or convexity condition on $L$, we present an existence theorem by means of the integro-extremal technique. We also discuss the monotonicity property of the minimizers. An application to the extended Fisher-Kolmogorov model is included.
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