Eigenvalue Problems for Degenerate Nonlinear Elliptic Equations in Anisotropic Media

  title={Eigenvalue Problems for Degenerate Nonlinear Elliptic Equations in Anisotropic Media},
  author={Dumitru Motreanu and Vicentiu D. Radulescu},
We study nonlinear eigenvalue problems of the type −div(a(x)∇u) = g(λ,x,u) in RN , where a(x) is a degenerate nonnegative weight. We establish the existence of solutions and we obtain information on qualitative properties as multiplicity and location of solutions. Our approach is based on the critical point theory in Sobolev weighted spaces combined with a Caffarelli-Kohn-Nirenberg-type inequality. A specific minimax method is developed without making use of Palais-Smale condition. 


Publications referenced by this paper.
Showing 1-10 of 27 references

Variational and Non-Variational Methods in Nonlinear Analysis and Boundary Value Problems

  • D. Motreanu, V. Rădulescu
  • Nonconvex Optimization and Its Applications, vol…
  • 2003

Nonlinear eigenvalue problems for quasilinear operators on unbounded domains

  • E. Montefusco, V. Rădulescu
  • NoDEA Nonlinear Differential Equations Appl. 8
  • 2001
1 Excerpt

The Hardy inequality and the asymptotic behaviour of the heat equation with an inverse-square potential

  • J. L. Vazquez, E. Zuazua
  • J. Funct. Anal. 173
  • 2000
1 Excerpt

On the Ca ff arelliKohnNirenberg inequalities : sharp constants , existence ( and nonexistence ) , and symmetry of extremal functions

  • F. Catrina, Z.-Q. Wang
  • Comm . Pure Appl . Math .
  • 1999

On the existence of extremal functions for a weighted Sobolev embedding with critical exponent

  • P. Caldiroli, R. Musina
  • Calc. Var. Partial Differential Equations 8
  • 1999
2 Excerpts

A review of Hardy inequalities

  • E. B. Davies
  • The Maz’ya Anniversary Collection, Vol. 2
  • 1998
1 Excerpt

Hardy’s inequalities revisited

  • H. Brezis, M. Marcus
  • Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997…
  • 1998
1 Excerpt

A saddle point approach to nonlinear eigenvalue problems

  • D. Motreanu
  • Math. Slovaca 47
  • 1997
1 Excerpt

Similar Papers

Loading similar papers…