Nonlinear discrete Sturm–Liouville problems

Numerical Discrete Algorithm for Some Nonlinear Problems

In this paper we use the eigenfunctions of the Laplacian to approximate the solution of some nonlinear equations which are used to model natural phenomena (as the Navier-Stokes flow equations, for instance). In this respect we propose a numerical algorithm, combining the Uzawa and Arrow-Hurwitz algorithms. The algorithm proposed here shares features from both algorithms, and it has the followin...

Multiscale analysis for nonlinear variational problems arising from discrete systems

The object of this thesis is the study of high density discrete systems as variational limit of low density discrete energies indexed by the number of nodes of the system itself. In this context the term discreteness should be understood rather broadly as inferring to different scales from crystal lattice to grain structure while the low-to-high density limit refers to the discrete-to-continuum...

On discrete maximum principles for nonlinear elliptic problems

Nonlinear Discrete Periodic Boundary Value Problems at Resonance

The Discrete Lagrangian Theory and Its Application to Solve Nonlinear Discrete Constrained Optimization Problems

In this research we present new results on discrete Lagrangian methods (DLM) and extend our previous (incomplete and highly simpli ed) theory on the method. Our proposed method forms a strong mathematical foundation for solving general nonlinear discrete optimization problems. Speci cally, we show for continuous Lagrangian methods the relationship among local minimal solutions satisfying constr...