Symmetry breaking and semilinear elliptic equations (Q1122961)

Symmetry breaking bifurcations (SBB's) are studied which occur on the radially symmetric solution branches of the semilinear elliptic equation \(\Delta u+\lambda f(u)=0\) on the unit ball in the space \(R^ 3\). A general theory is developed which permits a straightforward calculation of the SBB's. The theory is then applied to numerically study branches of SBB's when the function f(u) takes the form \(f(u)=u(1+| u|^{p- 1}),\) \(p>1\). In particular the dependence of the location of the SBB's on the value of p is investigated. Numerical results are included.