Multiplicity of bounded solutions to the $k$-Hessian equation with a Matukuma-type source
Multiplicity of bounded solutions to the $k$-Hessian equation with a Matukuma-type source
The aim of this paper is to deal with the k -Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problem (1)\quad\begin{cases} S_k(D^2u)= \lambda \,\frac{|x|^{\mu-2}}{(1+|x|^2)^{{\mu}/{2}}} \,(1-u)^q &\text{in } B,\\ u < 0 & \text{in } B,\\ u=0 &\text{on }\partial B, \end{cases} where …