@article{AIHPC_2009__26_6_2481_0, author = {Rossi, Luca}, title = {Liouville Type Results for Periodic and Almost Periodic Linear Operators}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {26}, year = {2009}, pages = {2481-2502}, doi = {10.1016/j.anihpc.2009.07.001}, mrnumber = {2569904}, zbl = {pre05649882}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_6_2481_0} }
Rossi, Luca. Liouville Type Results for Periodic and Almost Periodic Linear Operators. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 2481-2502. doi : 10.1016/j.anihpc.2009.07.001. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_6_2481_0/
[1] On Positive Solutions of Elliptic Equations With Periodic Coefficients in , Spectral Results and Extensions to Elliptic Operators on Riemannian Manifolds, in: Differential Equations, Birmingham, Alabama, 1983, North-Holland Math. Stud., vol. 92, North-Holland, Amsterdam, 1984, pp. 7-17. | MR 799327 | Zbl 0564.35033
,[2] Almost-Periodic Functions and Functional Equations, Van Nostrand Reinhold, New York, 1971. | MR 275061 | Zbl 0215.15701
, ,[3] Un Théorème De Liouville Pour Des Équations Elliptiques À Coefficients Périodiques, C. R. Acad. Sci. Paris Sér. I Math. 309 (5) (1989) 245-250. | MR 1010728 | Zbl 0691.35022
, ,[4] Superlinear Indefinite Elliptic Problems and Nonlinear Liouville Theorems, Topol. Methods Nonlinear Anal. 4 (1) (1994) 59-78. | MR 1321809 | Zbl 0816.35030
, , ,[5] Initial Blow-Up for the Solutions of a Semilinear Parabolic Equation With Source Term, in: Équations Aux Dérivées Partielles Et Applications, Gauthier-Villars/Éd. Sci. Méd. Elsevier, Paris, 1998, pp. 189-198. | MR 1648222 | Zbl 0914.35055
,[6] Beiträge Zur Theorie Der Fastperiodischen Funktionen, Math. Ann. 96 (1) (1927) 119-147. | JFM 52.0261.01 | MR 1512308
,[7] Zur Theorie Der Fastperiodischen Funktionen II. Zusammenhang Der Fastperiodischen Funktionen Mit Funktionen Von Unendlich Vielen Variabeln; Gleichmässige Approximation Durch Trigonometrische Summen, Acta Math. 46 (1-2) (1925) 101-214. | JFM 51.0212.02 | MR 1555201
,[8] Some Remarks on Liouville Type Theorems, in: Recent Advances in Nonlinear Analysis, World Sci. Publ., Hackensack, NJ, 2008, pp. 43-65. | MR 2410737 | Zbl pre05375300
, , ,[9] Fully Nonlinear Elliptic Equations, Amer. Math. Soc. Colloq. Publ., vol. 43, American Mathematical Society, Providence, RI, 1995. | MR 1351007 | Zbl 0834.35002
, ,[10] Hadamard and Liouville Type Results for Fully Nonlinear Partial Differential Inequalities, Commun. Contemp. Math. 5 (2003) 435-448. | MR 1992357 | Zbl 1040.35024
, ,[11] On the Liouville Property for Fully Nonlinear Equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2) (2000) 219-245. | Numdam | MR 1753094 | Zbl 0956.35035
, ,[12] Some Remarks on Liouville Type Results for Quasilinear Elliptic Equations, Proc. Amer. Math. Soc. 131 (6) (2003) 1891-1899, (electronic). | MR 1955278 | Zbl 1076.35038
, ,[13] Sulla Differenziabilità E L'analiticità Delle Estremali Degli Integrali Multipli Regolari, Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. (3) 3 (1975) 25-43. | Zbl 0084.31901
,[14] Almost Periodic Differential Equations, Lecture Notes in Math., vol. 377, Springer-Verlag, Berlin, 1974. | MR 460799 | Zbl 0325.34039
,[15] A Priori Bounds for Positive Solutions of Nonlinear Elliptic Equations, Comm. Partial Differential Equations 6 (8) (1981) 883-901. | MR 619749 | Zbl 0462.35041
, ,[16] On Isolated Singularities of Solutions of Second Order Elliptic Differential Equations, J. Anal. Math. 4 (1955/1956) 309-340. | MR 81416 | Zbl 0071.09701
, ,[17] Elliptic Partial Differential Equations of Second Order, Grundlehren Math. Wiss., vol. 224, second ed., Springer-Verlag, Berlin, 1983. | MR 737190 | Zbl 0562.35001
, ,[18] Liouville Theorems for Nonlinear Parabolic Equations of Second Order, Differential Integral Equations 9 (1) (1996) 149-172. | MR 1364039 | Zbl 0840.35043
, ,[19] On a Question in the Theory of Almost Periodic Differential Equations, Proc. Amer. Math. Soc. 127 (9) (1999) 2665-2670. | MR 1485481 | Zbl 0924.34039
, ,[20] Almost Periodicity of Solutions for Almost Periodic Evolution Equations, Differential Integral Equations 18 (4) (2005) 469-480. | MR 2122710
, ,[21] Integral Representations and Liouville Theorems for Solutions of Periodic Elliptic Equations, J. Funct. Anal. 181 (2) (2001) 402-446. | MR 1821702 | Zbl 0986.35028
, ,[22] Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr., vol. 23, American Mathematical Society, Providence, RI, 1967, translated from the Russian by S. Smith. | MR 241822 | Zbl 0174.15403
, , ,[23] Polynomial Growth Solutions of Uniformly Elliptic Operators of Non-Divergence Form, Proc. Amer. Math. Soc. 129 (12) (2001) 3691-3699, (electronic). | MR 1860504 | Zbl 0989.35042
, ,[24] Liouville-Type Theorems and Harnack-Type Inequalities for Semilinear Elliptic Equations, J. Anal. Math. 90 (2003) 27-87. | MR 2001065 | Zbl 1173.35477
, ,[25] Second Order Parabolic Differential Equations, World Scientific Publishing, River Edge, NJ, 1996. | MR 1465184 | Zbl 0884.35001
,[26] A Counterexample in the Theory of Almost Periodic Differential Equations, Rocky Mountain J. Math. 25 (1) (1995) 437-440. | MR 1340018 | Zbl 0833.34041
, , ,[27] On a Liouville-Type Theorem for Linear and Nonlinear Elliptic Differential Equations on a Torus, Bull. Braz. Math. Soc. (N.S.) 23 (1-2) (1992) 1-20. | MR 1203171 | Zbl 0787.35028
, ,[28] Stability and Almost Periodicity of Trajectories of Periodic Processes, J. Differential Equations 115 (2) (1995) 402-415. | MR 1310938 | Zbl 0815.34050
,[29] Positive Harmonic Functions and Diffusion, Cambridge Stud. Adv. Math., vol. 45, Cambridge University Press, Cambridge, 1995. | MR 1326606 | Zbl 0858.31001
,[30] Second Order Elliptic Operators With Periodic Coefficients: Criticality Theory, Perturbations, and Positive Harmonic Functions, J. Funct. Anal. 129 (1) (1995) 80-107. | MR 1322643 | Zbl 0826.35030
,[31] Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1967. | MR 219861 | Zbl 0153.13602
, ,[32] Non-Existence of Positive Solutions of Fully Nonlinear Elliptic Equations in Unbounded Domains, Commun. Pure Appl. Anal. 7 (1) (2008) 125-141. | MR 2358359 | Zbl pre05286458
,[33] Elliptic Differential Equations and Obstacle Problems, Plenum Press, New York, 1987. | MR 1094820 | Zbl 0655.35002
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