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Critical points of convex perturbations of some indefinite quadratic forms and semilinear boundary value problems at resonance. (English) Zbl 0678.35091

Summary: Critical points of convex perturbations of indefinite quadratic forms are obtained from the dual least action principle. The main result leads to necessary and sufficient conditions for the existence of a critical point when the corresponding Euler equation is scalar or when the perturbation is strictly convex. Applications are given to periodic solution of Hamiltonian systems and to systems of semilinear beam equations. A global version of the averaging method is given.

MSC:

35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
47A50 Equations and inequalities involving linear operators, with vector unknowns
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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