• Corpus ID: 235490071

Singular solutions to $k$-Hessian equations with fast-growing nonlinearities

@inproceedings{JoaoMarcosdo2021SingularST,
  title={Singular solutions to \$k\$-Hessian equations with fast-growing nonlinearities},
  author={'O JoaoMarcosdo and Evelina Shamarova and Esteban da Silva},
  year={2021}
}
We study a class of elliptic problems, involving a k-Hessian and a very fast-growing nonlinearity, on a unit ball. We prove the existence of a radial singular solution and obtain its exact asymptotic behavior in a neighborhood of the origin. Furthermore, we study the multiplicity of regular solutions and bifurcation diagrams. An essential ingredient of this study is analyzing the number of intersection points between the singular and regular solutions for rescaled problems. In the particular… 

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