Article Contents
Article Contents

Existence and monotonicity property of minimizers of a nonconvex variational problem with a second-order Lagrangian

• A variational problem

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.

Mathematics Subject Classification: Primary: 49K15, Secondary: 49J45.

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