Abstract
AbstractLet{(M,g)}be a smooth compact Riemannian manifold of dimension{n\geq 5}. We are concerned with the following elliptic problem:-\Delta_{g}u+a(x)u=u^{\frac{n+2}{n-2}+\varepsilon},\quad u>0\text{ in }M,where{\Delta_{g}=\mathrm{div}_{g}(\nabla)}is the Laplace–Beltrami operator onM,{a(x)}is a{C^{2}}function onMsuch that the operator{-\Delta_{g}+a}is coercive, and{\varepsilon>0}is a small real parameter. Using the Lyapunov–Schmidt reduction procedure, we obtain that the problem under consideration has ak-peaks solution for positive integer{k\geq 2}, which blow up and concentrate at one point inM.
Highlights
Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 5, where g denotes the metric tensor
Using the Lyapunov–Schmidt reduction procedure, we obtain that the problem under consideration has a k-peaks solution for positive integer k ≥ 2, which blow up and concentrate at one point in M
We are interested in the following supercritical elliptic problem:
Summary
Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 5, where g denotes the metric tensor. There are many results about the existence and properties of solutions for nonlinear elliptic equations on compact Riemannian manifolds.
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