论文信息 - BIFURCATION OF POSITIVE SOLUTIONS FOR A SEMILINEAR EQUATION WITH CRITICAL SOBOLEV EXPONENT

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 u = u u p + u 2 1 , u > 0, in , u = 0, on @ . where R n , n 3 is a bounded C 2 -domain > 1, 1 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.

Yuanji Cheng

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