Unit description:

The main goals of this Research Unit are twofold: on the one hand, we try to show some tools and methods of nonlinear functional analysis to study nonlinear elliptic equations; and on the other hand, to present some applications of these results to specific problems arising from population dynamics.

Specifically, we describe monotony methods, variational methods (minima, the mountain pass theorem) and local and global bifurcations. Of course, a review of linear theory (existence, uniqueness, regularity, maximum principle) is mandatory.

These methods will be extensively applied to different examples and models.

Course program:

  • Linear elliptic problems. Maximum principle.
  • The sub-supersolution method. Variational methods. Local and global bifurcations.
  • Elliptic Problems arising in population dynamics.
  • Kirchhoff-Nonlocal elliptic equations.
  • Elliptic equations with critical growth in the gradient.

Lectures:

  • David Arcoya (Universidad de Granada)
  • Antonio Suárez Fernández (Universidad de Sevilla)
  • Salvador Villegas (Universidad de Granada)
  • José Carmona (Universidad de Granada)

Conference Speakers:

  • Joao R. Santos Junior (Universidad Federal de Pará, Brasil).
    Title: "Ground state solutions of Elliptic PDE's via minimization on the Nehari Manifold".
    Thursday, April 19, 15:30 - 16:30.
    Slides of the talk (pdf)

Schedule of the Course 4:

  • Wednesday, April 18: 10:00-11:30 and 12:00-13:30 (Antonio Suárez)
  • Thursday, April 19: 10:00-11:30 and 12:00-13:30 (Salvador Villegas)
  • Friday, April 20: 10:00-11:30 and 12:00-13:30 (José Carmona)
  • Monday, April 23: 12:00-13:30 and 16:30-18:00 (David Arcoya)