Symmetry properties of solutions to some nonlinear Schroedinger equations are investigated. In particular, here the Laplace operator is perturbed by singular potentials which do not belong to the Kato class. A result of symmetry breaking of solutions is obtained provided a preliminary theorem about biradial solutions is stated. Further, a problem involving the biharmonic operator and exponential nonlinearity in dimension 4 is studied, connecting degree counting formulas with direct methods of calculus of variations via Morse theory and deformation lemmas.
(2011). Multiplicity of solutions to elliptic equations the case of singular potentials in second order problems and morse theory in a fourth order problem. (Tesi di dottorato, Università degli Studi di Milano-Bicocca, 2011).
Multiplicity of solutions to elliptic equations the case of singular potentials in second order problems and morse theory in a fourth order problem
ABATANGELO, LAURA
2011
Abstract
Symmetry properties of solutions to some nonlinear Schroedinger equations are investigated. In particular, here the Laplace operator is perturbed by singular potentials which do not belong to the Kato class. A result of symmetry breaking of solutions is obtained provided a preliminary theorem about biradial solutions is stated. Further, a problem involving the biharmonic operator and exponential nonlinearity in dimension 4 is studied, connecting degree counting formulas with direct methods of calculus of variations via Morse theory and deformation lemmas.
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