| Bifurcation, a-priori bound and negative solutions for the complex Hessian equation |
| Hua Luo,Guowei Dai |
| Keywords:Bifurcation; A-priori bound; Complex Hessian equation |
| Abstract: |
| This paper establishes global bifurcation and eigenvalue results for the following complex $k$-Hessian equation
\begin{equation}
\left\{
\begin{array}{ll}
S_k\left(u_{i\overline{j}}\right)=\lambda^k f(-u)\,\, &\text{in}\,\, B,\u=0 &\text{on}\,\, \partial B.
\end{array}
\right.\nonumber
\end{equation}
The existence/nonexistence, uniqueness and multiplicity of radially symmetric negative solutions are investigated. Moreover, a-priori bound of radially symmetric negative solutions is also obtained. |
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