Variational methods for strongly indefinite problems

Variational Methods for Strongly Indefinite Problems

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An Index Theory for Paths That Are Solutions of a Class of Strongly Indefinite Variational Problems

We generalize the Morse index theorem of [12, 13] and we apply the new result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of semi-Riemannian manifolds. More specifically, we consider semi-Riemannian manifolds (M, g) admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distr...

A Survey of Direct Methods for Solving Variational Problems

This study presents a comparative survey of direct methods for solving Variational Problems. Thisproblems can be used to solve various differential equations in physics and chemistry like RateEquation for a chemical reaction. There are procedures that any type of a differential equation isconvertible to a variational problem. Therefore finding the solution of a differential equation isequivalen...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Generalized DG-Methods for Highly Indefinite Helmholtz Problems based on the Ultra-Weak Variational Formulation

We develop a stability and convergence theory for the Ultra Weak Variational Formulation (UWVF) of a highly indefinite Helmholtz problem in Rd, d ∈ {1, 2, 3}. The theory covers conforming as well as nonconforming generalized finite element methods. In contrast to conventional Galerkin methods where a minimal resolution condition is necessary to guarantee the unique solvability, it is proved tha...