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Entire solutions for some critical equations in the Heisenberg group

Pucci Patrizia, Temperini Letizia

Opuscula Mathematica

2022

Vol. 42, no. 2

279--303

We complete the study started in the paper [P. Pucci, L. Temperini, On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces, Math. Eng. 5 (2023), Paper no. 007], giving some applications of its abstract results to get existence of solutions of certain critical equations in the entire Heinseberg group. In particular, different conditions for existence are given for critical horizontal p-Laplacian equations.

Some recent results on singular p-Laplacian equations

Guarnotta Umberto, Livrea Roberto, Marano Salvatore A.

Demonstratio Mathematica

2022

Vol. 55, nr 1

416--428

A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided.

Existence and multiplicity results for quasilinear equations in the Heisenberg group

Pucci Patrizia

Opuscula Mathematica

2019

Vol. 39, no. 2

247--257

In this paper we complete the study started in [Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019)] on entire solutions for a quasilinear equation [formula] in Hn, depending on a real parameter λ, which involves a general elliptic operator A in divergence form and two main nonlinearities. Here, in the so called sublinear case, we prove existence for all λ > 0 and, for special elliptic operators A, existence of infinitely many solutions [formula].

The frequency of the zeros of some differential polynomials

Belaïdi B.

Demonstratio Mathematica

2013

Vol. 46, nr 1

75--86

Let ρp(ƒ) and σp(ƒ) denote respectively the iterated p-order and the iterated p-type of an entire function ƒ. In this paper, we study the iterated order and the fixed points of some differential polynomials generated by solutions of the differential equation f''+A1(z)f'+A0(z)f=0 where A1(z), A0(z) are entire functions of finite iterated p-order such that ρp(A1) = ρp(A0) = ρ(0< ρ <+∞) and σp(A1)< σp(A0) =σ(0< σ <+∞).

Entire solutions of a functional equation of pxider type

Smajdor W.

Demonstratio Mathematica

2002

Vol. 35, nr 3

572-582