Special Issue in honor of Alan C. Lazer. Electron. J. Diff. Eqns., Special Issue 01 (2021), pp. 149-167.

Oscillatory solutions and critical exponents for fully nonlinear equations

Filomena Pacella, David Stolnicki

Abstract:
We study existence and nonexistence of radial positive solutions for a class of fully nonlinear equations involving Pucci's extremal operators. By analyzing the periodic orbits of an associated dynamical system we are able to give estimates on the range of the exponents for which entire oscillating solutions exist. This, in turn, allows to improve previous bounds on the critical exponents defined in [2].

Published October 6, 2021.
Math Subject Classifications: 35J15, 35J60, 35B09, 34C25.
Key Words: Fully nonlinear equations; radial solutions; critical exponents; dynamical systems.
DOI: https://doi.org/10.58997/ejde.sp.01.p1

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Filomena Pacella
Dipartimento di Matematica
Universityà di Roma Sapienza, Italy
email: pacella@mat.uniroma1.it
David Stolnicki
Dipartimento di Matematica
Universityà di Roma Sapienza, Italy
email: david.stolnicki@uniroma1.it

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