The uniqueness of the linearly stable positive solution for a class of superlinear indefinite problems with nonhomogeneous boundary conditions Articles uri icon

publication date

  • August 2013

start page

  • 503

end page

  • 523


  • 3


  • 255

International Standard Serial Number (ISSN)

  • 0022-0396

Electronic International Standard Serial Number (EISSN)

  • 1090-2732


  • This paper proves the uniqueness of the positive linearly stable steady-state for a paradigmatic class of superlinear indefinite parabolic problems arising in population dynamics, under non-homogeneous Dirichlet conditions on the boundary of the domain. The result is absolutely non-trivial, since examples are known for which the model admits an arbitrarily large number of steady-states. Our proof is based on some local and global continuation techniques. Optimal existence and multiplicity results are also obtained through some additional monotonicity and topological techniques.


  • uniqueness of linearly stable steady-states; super linear indefinite problems; a priori bounds; optimal multiplicity