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In the present paper we survey some recents results concerning existence of semiclassical standing waves solutions for nonlinear Schrödinger equations. Furthermore, from Maxwell's equations we derive a nonlinear Schrödinger equation which represents a model of propagation of an electromagnetic field in optical waveguides.

Metrics with only finitely many isometry invariant geodesics.

Hans-Bert Rademacher (1989)

Mathematische Annalen

Minimal Graphs.

James Eells (1979)

Manuscripta mathematica

Minimal surfaces and deformations of holomorphic curves in Kähler-Einstein manifolds

Claudio Arezzo (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Minimal surfaces and the affine Toda field model.

John Bolton, Franz Pedit, L. Woodward (1995)

Journal für die reine und angewandte Mathematik

Minimal surfaces via loop groups.

Dorfmeister, J., Pedit, F., Toda, M. (1997)

Balkan Journal of Geometry and its Applications (BJGA)

Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems

Andrzej Szulkin (1986)

Annales de l'I.H.P. Analyse non linéaire

Minimax theorems on $C^{1}$ manifolds via Ekeland variational principle.

Cuesta, Mabel (2003)

Abstract and Applied Analysis

Minimization problems with lack of compactness

Michel Willem (1996)

Banach Center Publications

Minimizers of Dirichlet functionals on the $n$ -torus and the weak KAM theory

G. Wolansky (2009)

Annales de l'I.H.P. Analyse non linéaire

Minimizing energy among homotopic maps.

Miao, Pengzi (2004)

International Journal of Mathematics and Mathematical Sciences

Minimizing Harmonic Mappings form a surface perfored with small holes into a riemannian manifold.

Sami Baraket, Dong Ye (1992)

Manuscripta mathematica

Minimizing $p$ -harmonic maps at a free boundary

Frank Duzaar, Andreas Gastel (1998)

Bollettino dell'Unione Matematica Italiana

Studiamo le proprietà di regolarità delle mappe fra varietà di Riemann che minimizzano la $p$ -energia fra quelle che soddisfano una condizione di frontiera pazialmente libera. Proviamo che tali mappe sono Hölder continue vicino alla frontiera libera fuori di un insieme singolare, e otteniamo stime ottimali per la dimensione di Hausdorff di questo insieme singolare.

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