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Dual variational methods in critical point theory and applications
This paper contains some general existence theorems for critical points of a continuously differentiable functional I on a real Banach space. The strongest results are for the case in which I isExpand
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Critical point theorems for indefinite functionals
A variational principle of a minimax nature is developed and used to prove the existence of critical points for certain variational problems which are indefinite. The proofs are carried out directlyExpand
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Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials
Received by the editors November 27, 1990. 1991 Mathematics Subject Classification. Primary 34C99, 58E99, 58F99. The first author was supported by Ministero P. I. gruppo 40% "Calcolo delleExpand
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Periodic and heteroclinic orbits for a periodic hamiltonian system
Abstract Consider the Hamiltonian system: (★) q ¨ + V ′ ( q ) = 0 where q = (q1,…, qn) and V is periodic in qi, 1 ≦ i ≦ n. It is known that (★) then possesses at least n + 1 equilibrium solutions.Expand
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Some Critical Point Theorems and Applications to Semilinear Elliptic Partial Differential Equations.
Abstract : Variational methods are used to obtain some new existence theorems for critical points of a real valued function on a Banach space. Applications are made to semilinear elliptic boundaryExpand
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Mixed states for an Allen‐Cahn type equation
This paper continues the recent study of an Allen-Cahn model PDE [1] by eliminating a strong spatial reversibility condition and by weakening certain nondegeneracy conditions on families of basicExpand
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A minimax method for a class of Hamiltonian systems with singular potentials
Abstract This paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of Hamiltonian systems when a singular potential is present. TheExpand
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A note on topological degree for potential operators
Let E be a real Hilbert space and T: E -+ E be a compact potential operator with T(u) = t’(u) where t: E -+ IF!. Let g(u) = $ /I u II2 t(u). Our main goal in this note is to show that the index of anExpand
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Periodic solutions of Hamiltonian systems of 3-body type
Abstract We study the question of the existence of periodic solutions of Hamiltonian systems of the form: (✶) q ¨ + V q ( t , q ) = 0 where V = ∑ 1 ≦ i ≠ j 3 V i j ( t , q i − q j ) with V(t, ξ)Expand
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A rapid convergence method for a singular perturbation problem
Abstract The existence of spatially periodic solutions for a singular perturbation of elliptic type is established. A rapid convergence method is used to obtain the result.
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