Non-radial solutions with orthogonal subgroup invariance for semilinear Dirichlet problems

Ryuji Kajikiya

DOI: http://dx.doi.org/10.12775/TMNA.2003.003

Abstract


A semilinear elliptic equation, $-\Delta u=\lambda f(u)$, is studied in a ball
with the Dirichlet boundary condition. For a closed subgroup $G$ of the
orthogonal group, it is proved that the number of non-radial $G$ invariant solutions
diverges to infinity as $\lambda$ tends to $\infty$ if $G$
is not transitive on the unit sphere.

Keywords


Semilinear elliptic equation; group invariant solution; non-radial solution; variational method

Full Text:

FULL TEXT

Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism