Existence and multiplicity results for quasilinear equations in the Heisenberg group

• Autorzy: Pucci Patrizia

Identyfikatory

DOI

10.7494/OpMath.2019.39.2.247

• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Heisenberg group; entire solutions; critical exponents

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2019
• Tom: Vol. 39, no. 2
• Strony: 247--257
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Pucci Patrizia

• Universita degli Studi di Perugia Dipartimento di Matematica e Informatica Via Vanvitelli 1, 06123 Perugia, Italy

Bibliografia

• [1] G. Autuori, P. Pucci, Existence of entire solutions for a class of quasilinear elliptic equations, NoDEA Nonlinear Differential Equations Appl. 20 (2013), 977-1009.
• [2] S. Bordoni, P. Pucci, Schrodinger-Hardy systems involving two Laplacian operators in the Heisenberg group, Bull. Sci. Math. 146 (2018), 50-88.
• [3] N. Garofalo, E. Lanconelli, Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation, Ann. Inst. Fourier 40 (1990), 313-356.
• [4] L. Hórmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171.
• [5] S.P. Ivanov, D.N. Vassilev, Extremals for the Sobolev inequality and the quaternionic contact Yarnabe problem, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2011.
• [6] G.P. Leonardi, S. Masnou, On the isoperimetric problem in the Heisenberg group Hn, Ann. Mat. Pura Appl. 184 (2005), 533-553.
• [7] G. Molica Bisci, P. Pucci, Critical Dirichlet problems on H domains of Carnot groups, Two nonlinear days in Urbino 2017, Electron. J. Diff. Eqns., Special Volume dedicated to the memory of Anna Aloe, Conf. 25 (2018), 179-196.
• [8] P. Pucci, Critical Schrodinger-Hardy systems in the Heisenberg group, Discrete Contin. Dyn. Syst. Ser. S, Special Issue on the occasion of the 60th birthday of Professor Vicentiu D. Radulescu, 12 (2019), 375-400.
• [9] P. Pucci, Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019).
• [10] P. Pucci, V. Radulescu, Combined effects in quasilinear elliptic problems with lack of compactness, Rend. Lincei Mat. Appl., Special volume dedicated to the memory of Professor Giovanni Prodi, 22 (2011), 189-205.
• [11] P. Pucci, Q. Zhang, Existence of entire solutions for a class of variable exponent elliptic equations, J. Differential Equations 257 (2014), 1529-1566.
• [12] M. Struwe, Variational Methods, Applications to nonlinear partial differential equations and Hamiltonian systems, 4th ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, A Series of Modern Surveys in Mathematics 34, Springer-Verlag, Berlin, 2008