Large energy entire solutions for the Yamabe equation

Large energy entire solutions for the Yamabe type problem of polyharmonic operator

In this paper, we consider the following Yamabe type problem of polyharmonic operator : { Dmu = |u| 4m N−2m u on S u ∈ H(S ), (P ) where N ≥ 2m + 1,m ∈ N+, S is the unit sphere with the induced Riemannian metric g = gSN , and Dm is the elliptic differential operator of 2m order given by Dm = m ∏ k=1 (−∆g + 14(N − 2k)(N + 2k − 2)) where ∆g is the Laplace-Beltrami operator on S . We will show tha...

Blow-up Solutions for Linear Perturbations of the Yamabe Equation

For a smooth, compact Riemannian manifold (M, g) of dimension N ≥ 3, we are interested in the critical equation ∆gu+ ( N − 2 4(N − 1) Sg +εh ) u = u N+2 N−2 in M , u > 0 in M , where ∆g is the Laplace–Beltrami operator, Sg is the Scalar curvature of (M, g), h ∈ C (M), and ε is a small parameter.

Square-integrability of solutions of the Yamabe equation

We show that solutions of the Yamabe equation on certain ndimensional non-compact Riemannian manifolds which are bounded and Lp for p = 2n/(n−2) are also L2. This Lp-L2-implication provides explicit constants in the surgery-monotonicity formula for the smooth Yamabe invariant in our article [1]. As an application we see that the smooth Yamabe invariant of any 2connected compact 7-dimensional ma...

The entire large solutions for a quasilinear Schrödinger elliptic equation by the dual approach

Entire Solutions of a Fully Nonlinear Equation