Currently displaying 1 – 4 of 4

Showing per page

Order by Relevance | Title | Year of publication

Eigenvalue problems with indefinite weight

Andrzej SzulkinMichel Willem — 1999

Studia Mathematica

We consider the linear eigenvalue problem -Δu = λV(x)u, u D 0 1 , 2 ( Ω ) , and its nonlinear generalization - Δ p u = λ V ( x ) | u | p - 2 u , u D 0 1 , p ( Ω ) . The set Ω need not be bounded, in particular, Ω = N is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues λ n .

Symmetry of solutions of semilinear elliptic problems

Jean Van SchaftingenMichel Willem — 2008

Journal of the European Mathematical Society

We study symmetry properties of least energy positive or nodal solutions of semilinear elliptic problems with Dirichlet or Neumann boundary conditions. The proof is based on symmetrizations in the spirit of Bartsch, Weth and Willem (J. Anal. Math., 2005) together with a strong maximum principle for quasi-continuous functions of Ancona and an intermediate value property for such functions.

Page 1

Download Results (CSV)