On Liouville type theorems for second order elliptic differential equations
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 22 (1995) no. 2, p. 275-298 
@article{ASNSP_1995_4_22_2_275_0,
     author = {Karp, Lavi},
     title = {On Liouville type theorems for second order elliptic differential equations},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 22},
     number = {2},
     year = {1995},
     pages = {275-298},
     zbl = {0840.35025},
     mrnumber = {1354908},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1995_4_22_2_275_0}
}

Karp, Lavi. On Liouville type theorems for second order elliptic differential equations. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 22 (1995) no. 2, pp. 275-298. http://www.numdam.org/item/ASNSP_1995_4_22_2_275_0/

[1] R.A. Adams, Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[2] S. Agmon, On Positivity and decay of solutions of second order elliptic equations on Riemannian manifolds, Methods of Functional Analysis and Theory of Elliptic Equations (D. Greco ed.), Liguari Editore, Napoli, 1982, 19-52. | MR 819005 | Zbl 0595.58044

[3] M. Avellaneda - F.H. Lin, Une théorème de Liouville pour des équations elliptiques à coefficients périodiques, C. R. Acad. Sci. Paris Sér. I Math. 309 (1989), 245-250. | MR 1010728 | Zbl 0691.35022

[4] M. Avellaneda - F.H. Lin, LP bounds on singular integrals in homogenization, Comm. Pure Appl. Math. 44 (1991), 897-910. | MR 1127038 | Zbl 0761.42008

[5] H. Begehr - G.N. Hile, Schauder estimates and existence theory of entire solutions of linear elliptic operator, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 101-123. | MR 963845 | Zbl 0674.35019

[6] Yu. V. Egorov - M.A. Shubin, Linear Partial Differential Equations. Foundations of Classical Theory, Partial Differential Equations I (Yu. V. Egorov and M.A. Shubin, eds), Encyclopedia of Math. Sci., 30, Springer-Verlaga, Berlin-Heildelberg-New York, 1991. | MR 1141631 | Zbl 0738.35001

[7] A. Friedman, Bounded entire solutions of elliptic equations, Pacific J. Math. 44 (1973), 497-507. | MR 320506 | Zbl 0256.35024

[8] L. Karp, Generalized Newton potential and its applications, J. Math. Anal. Appl. 174 (1993), 480-497. | MR 1215629 | Zbl 0779.31004

[9] R.B. Lockhart, Fredholm properties of a class of elliptic operators on non-compact manifolds, Duke Math. J. 48 (1981), 289-312. | MR 610188 | Zbl 0486.35027

[10] R.B. Lockhart - R.C. Mcowen, On elliptic system in Rn, Acta Math. 150 (1983), 125-135. | MR 697610 | Zbl 0517.35031

[11] R.C. Mcowen, The behavior of the Laplacian on weighted Sobolev spaces, Comm. Pure Appl. Math. 32 (1979), 785-795. | MR 539158 | Zbl 0426.35029

[12] R.C. Mcowen, On elliptic operators in Rn, Comm. Partial Differential Equations 5 (1980), 913-933. | MR 584101 | Zbl 0448.35042

[13] N. Meyers, An expansion about infinity for solutions of linear elliptic equations, J. Math. Mech. 12 (1963), 247-264. | MR 149072 | Zbl 0121.32202

[14] C. Miranda, Partial Differential Equations of Elliptic Type, second edition, Springer-Verlag, Berlin-Heildelberg -New York, 1970. | MR 284700 | Zbl 0198.14101

[15] J. Moser - M. Struwe, On a Liouville type theorem for linear and nonlinear equations on a tours, Bol. Soc. Brasil. Mat. 23 (1992), 1-20. | MR 1203171 | Zbl 0787.35028

[16] M. Murata, Isomorphism theorems for elliptic operators in Rn, Comm. Partial Differential Equations 9 (1984), 1085-1105. | MR 759238 | Zbl 0556.47027

[17] M. Murata, On construction of Martin boundaries for second order elliptic equations, Publ. Res. Inst. Math. Sci. 26 (1990), 585-627. | MR 1081506 | Zbl 0726.31009

[18] L. Nirenberg - H.F. Walker, The null spaces of elliptic partial differential operators in Rn, J. Math. Anal. Appl. 42 (1973), 271-301. | MR 320821 | Zbl 0272.35029

[19] Y. Pinchover, On positive solutions of second second order elliptic equations, stability results and classification, Duke Math. J. 57 (1988), 955-980. | MR 975130 | Zbl 0685.35035

[20] Y. Pinchover, On the equivalence Green functions of second order elliptic equations in Rn, Differential Integral Equation 5 (1992), 481-493. | MR 1157482 | Zbl 0772.35015

[21] A. Pliś, A smooth linear elliptic differential equations without any solution in a sphere, Comm. Pure Appl. Math. 14 (1961), 599-617. | MR 136846 | Zbl 0163.13103

[22] M. Schecter, Principles of Functional Analysis, Academic Press, New York, 1971. | MR 445263 | Zbl 0211.14501

[23] E. Stein - G. Weiss, Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, New Jersey, 1971. | MR 304972 | Zbl 0232.42007