Minimization problems with lack of compactness
Periodic solutions of non-autonomous Hamiltonian systems with symmetries.
Eigenvalue problems with indefinite weight
We consider the linear eigenvalue problem -Δu = λV(x)u, , and its nonlinear generalization , . The set Ω need not be bounded, in particular, is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues .
Symmetry of solutions of semilinear elliptic problems
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.
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