Obiective si Activitati

  1. Rigorous definition of poly­harmonic operators with variable exponent and use of combined methods (minimization, variational principles) for the study of spectral properties.
  2. Study of mountain pass geometry properties of the energy functional, Pokhozaev­Pucci­Serrin identities, nonexistence results.
  3. Lack of compactness for anisotropic problems with variable exponent and formulation of related concentration­compactness principles.
  4. Development of the abstract framework, gap phenomena, role of anisotropic exponents in the appearance of new properties.
  5. Qualitative properties of solutions, case of general nonlocal operators, application of combined methods in the mathematical analysis of solutions.
  6. Application of variational and topological methods in the analysis of nonlocal problems; differences with respect to the local setting.
  7. Study of noncompact bifurcation problems in the nonlocal framework: combined methods and new phenomena.
  8. Abstract setting and additional technical difficulties with respect to the isotropic case; application of the critical point theory and topological methods.
  9. Variational and topological methods in the study of singular solutions, Karamata theory for the study of their asymptotic behaviour.
  10. Properties of the new operator on fractals, variational methods in the study of singular phenomena and new properties.

Toate obiectivele proiectului, conform etapelor stabilite, au fost realizate, mai mult, au fost depasite tintele initiale. Dincolo de dezideratele stabilite au fost create bazele unor noi linii de cercetare. Acest lucru reiese din sectiunea Rezultate.