The existence of infinitely many boundary blow-up solutions to the \(p\)-\(k\)-Hessian equation (Q6133261)

The authors consider the boundary blow-up \(p\)-\(k\)-Hessian problem, given by \[ \sigma_k(\lambda(D_i(|Du|^{p-2}D_j u)))=H(|x|)f(u) x\in \Omega,\quad u=+\infty \text{ on } \partial \Omega, \] where \(k\in \{1,2,\dots,N\}\), \(\sigma_k(\lambda)\) is the \(k\)-Hessian operator, \(f\) is a locally Lipschitz continuous, increasing, and positive function, \(H \in C(\Omega)\) is positive in \(\Omega\) and may be singular on \(\partial \Omega,\) and \(\Omega\) is a ball in \(\mathbb{R}^N\) \((N\geq 2)\). They investigate the existence of infinitely many radial solutions for the above problem using the method of sub- and super-solutions. It should be noted that there is currently no study investigating the boundary blow-up solution of the \(p\)-\(k\)-Hessian problem on a bounded domain.