EXISTENCE OF MANY POSITIVE SOLUTIONS OF SEMILINEAR ELLIPTIC-EQUATIONS ON ANNULUS

We study the existence of many nonradial positive solutions in an annulus of RN. It is an improvement of results in C. V. Coffman (A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984), 429-437. An annulus is invariant under many group actions and these group actions act naturaly on the functional and leave the functional invariant. Therefore when we look for critical points of the functional we can restrict the functional to the manifold consisting of all fixed points under the group action. We are going to use different group actions to obtain critical points and furthermore we can distinguish them. © 1990.