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The Variational and WKB Methods
1994More often than not, it is impossible to find exact solutions to the eigenvalue problem of the Hamiltonian. One then turns to approximation methods, some of which will be described in this and the following chapters. In this section we consider a few examples that illustrate the variational method.
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Variational methods for Hamiltonian PDEs
2008We present recent existence results of periodic solutions for completely resonant nonlinear wave equations in which both "small divisor" difficulties and infinite dimensional bifurcation phenomena occur. These results can be seen as generalizations of the classical finite-dimensional resonant center theorems of Weinstein-Moser and Fadell-Rabinowitz ...
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2017
In this chapter we discuss the use of optimization techniques in the study of ordinary and partial differential equations. The key idea is that a differential equation may arise as a necessary condition satisfies by a critical point of a well-chosen functional.
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In this chapter we discuss the use of optimization techniques in the study of ordinary and partial differential equations. The key idea is that a differential equation may arise as a necessary condition satisfies by a critical point of a well-chosen functional.
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Variational and Lagrangian Methods in Viscoelasticity
1956The time history of a thermodynamic system perturbed from equilibrium under the assumption of linearity obeys certain differential equations. Starting from Onsager’s reciprocity relations we have shown [1] how they may be derived from generalized concepts of free energy and dissipation function.
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On the Variate Difference Method
Biometrika, 1923Karl Pearson, Ethel M. Elderton
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Direct Methods in the Calculus of Variations
2003Semi-Classical Theory Integrable Functions Sobolev Spaces Semicontinuity Quasi-Convex Functionals Quasi-Minima Regularity of Quasi-Minima First Derivatives Partial Regularity Higher Derivatives.
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1996
A review is given of my work on the Cluster Variation Method (CVM). The Cluster Consistency Method (CCM), which is the consistency approach equivalent to the Cluster Variation Method, is first presented and its equivalence to the variational approach is shown.
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A review is given of my work on the Cluster Variation Method (CVM). The Cluster Consistency Method (CCM), which is the consistency approach equivalent to the Cluster Variation Method, is first presented and its equivalence to the variational approach is shown.
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