Singular solutions to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si5.svg"><mml:mi>k</mml:mi></mml:math>-Hessian equations with fast-growing nonlinearities

We study a class of elliptic problems, involving $k$-Hessian and very fast-growing nonlinearity, on unit ball. prove the existence radial singular solution obtain its exact asymptotic behavior in neighborhood origin. Furthermore, we multiplicity regular solutions bifurcation diagrams. An essential ingredient this is analyzing number intersection points between for rescaled problems. In particular case exponential convergence to analyze depending parameter $k$ dimension $d$.