On a class of fully nonlinear elliptic equations in dimension two

Pacella, Filomena; Stolnicki, David

doi:10.1016/j.jde.2021.07.004

Cited by 3 publications

(6 citation statements)

References 14 publications

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“…In this article we refine the results obtained in [2] and [4] by extending the approach of [5] to higher dimensions. In this way, we obtain, on the one hand, information on the exponents p for which oscillating pseudo-slow decaying solutions do not exist; on the other hand, a better estimate of the critical exponents p * ± , as compared with [2].…”

Section: Theorem 12 ([2]supporting

confidence: 52%

“…It is entirely based on the study of the orbits of an associated quadratic dynamical system. The same approach has been used in [5] to define and give bounds for a critical exponent that can be defined for the operator M − λ,Λ in dimension N = 2. While analyzing the dynamical system (defined in Section 2) it is important to understand for which values of p periodic orbits exist.…”

Section: Theorem 12 ([2]mentioning

confidence: 99%

“…Indeed, this enters not only in detecting the presence of pseudo-slow decaying solutions of (1.1) but also to study the existence of fast decaying solutions. This idea was exploited in [5] to estimate the critical exponent in dimension two.…”

Section: Theorem 12 ([2]mentioning

confidence: 99%

“…Here we analyze the dynamical system (2.5) in the case of the operator M + λ,Λ , with the aim of providing estimates on the values of p for which periodic orbits do not exist. We follow the approach of [4] which was used in [5] in the bi-dimensional case.…”

Section: Associated Dynamical Systemsmentioning

confidence: 99%

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Oscillatory solutions and critical exponents for fully nonlinear equations

Pacella

Stolnicki

2021

ejde

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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]. For more information see https://ejde.math.txstate.edu/special/01/p1/abstr.html

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Section: Theorem 12 ([2]supporting

confidence: 52%

Section: Theorem 12 ([2]mentioning

confidence: 99%

Section: Theorem 12 ([2]mentioning

confidence: 99%

Section: Associated Dynamical Systemsmentioning

confidence: 99%

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Oscillatory solutions and critical exponents for fully nonlinear equations

Pacella

Stolnicki

2021

ejde

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“…We now prove the monotonicity and concavity properties of the regular solutions, deriving them directly by the dynamical systems ( 14) or (16), and not from the second order ODEs. Let Γ be the regular trajectory of ( 14) or ( 16) which comes out from N 0 .…”

Section: For the Pointmentioning

confidence: 95%

Classification of radial solutions for fully nonlinear equations with Hardy potential

Maia,

Nornberg,

Pacella

2024

DCDS

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We study existence, nonexistence and regularity of positive radial solutions for a class of nonlinear equations driven by Pucci extremal operators, power nonlinearity and Hardy weight. We classify both regular continuous nondifferentiable and singular solutions defined in radial domains, punctured or not. We also obtain critical threshold exponents for the solvability in the exterior of a ball, as well as uniqueness and symmetry in annuli. Our results are based on the behavior of the trajectories described through suitable dynamical systems on the plane, in addition to energy monotonicity and asymptotic analysis.

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