Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, III

We consider the problem: Deltau+u(p)=0 in Omega(R), u=0 on partial derivativeOmega(R), u>0 in Omega(R), where Omega(R)equivalent to{xis an element ofR(N)|R-1SN-1 was showed for large R. In this paper, it will be showed that more various types of solutions than those obtained in [5], which are close to a finite sum of locally minimal energy solutions in H-R(G) for some Gsubset ofO(N), appear as R-->infinity. Furthermore, we discuss possible types of solutions and show that any solution with exactly two local maximum points should be O(N-1)-symmetric for large R>0.X112sciescopu