Citation: | Hua Luo, Guowei Dai. BIFURCATION, A-PRIORI BOUND AND NEGATIVE SOLUTIONS FOR THE COMPLEX HESSIAN EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 937-963. doi: 10.11948/20200120 |
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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