BIFURCATION OF POSITIVE SOLUTIONS FOR A SEMILINEAR EQUATION WITH CRITICAL SOBOLEV EXPONENT

In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent -Delta u = lambda u-alpha u(p)+u(2*-1), u > 0, in Omega, u = 0, on partial derivative Omega. where Omega subset of R-n, n >= 3 is a bounded C-2- domain lambda > lambda(1), 1 < p < 2* - 1 = n+ 2/n- 2 and alpha > 0 is a bifurcation parameter. Brezis and Nirenberg [2] showed that a lower order (non-negative) perturbation can contribute to regain the compactness and whence yields existence of solutions. We study the equation with an indefinite perturbation and prove a bifurcation result of two solutions for this equation.