Mohamed Bekiri, Mohammed Elamine Sebih
In this paper, we investigate the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary. The existence result is assured under some geometric conditions.
This paper contains 8 sections, 10 theorems, 126 equations.
Theorem 1.1
Let $\left( M,g\right)$ be a compact Riemannian manifold of dimension $n>3$ with smooth boundary $\partial M\neq\emptyset$. Assume that $a,\,b,\, f\in C^{\infty}(M)$, with $a>0,\, f>0$ on $M$. Let $x_{0}\in \operatorname{Int}(M)$ be a point in the interior of $M$ such that $f\left( x_{0}\right) =\ there exist a positive real number $\lambda$ and a nontrivial solution $u=w+h\in H_{0}^{1}\left( M\
