Multipeak solutions for asymptotically critical elliptic equations on Riemannian manifolds Original Research Article

Let (M,g)(M,g) be a smooth compact Riemannian manifold of dimension n≥3n≥3. We are concerned with the following asymptotically critical elliptic problem equation(0.1) View the MathML sourceΔgu+a(x)u=u2∗−1−ε,u>0inM, Turn MathJax on where View the MathML sourceΔg=−divg(∇) is the Laplace–Beltrami operator on MM, a(x)a(x) is a C1C1 function on MM, View the MathML source2∗=2nn−2 denotes the Sobolev critical exponent, εε is a small real parameter such that εε goes to 0. We use the Lyapunov–Schmidt reduction procedure to obtain that the problem (0.1) has a kk-peaks solution for positive integer k≥2k≥2, which blow up and concentrate at some points in MM.