On positive Liouville theorems and asymptotic behavior of solutions of fuchsian type elliptic operators

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1. [1] S. Agmon, On positivity and Decay of Second Order Elliptic Equations on Riemannian Manifolds, Methods of Functional Analysis and Theory of Elliptic Equations, D. GRECO, Ed., Liguori, Naples, 1982, pp. 19-52. Zbl0595.58044MR819005
2. [2] H. Berestycki, L. Caffarelli and L. Nirenberg, Uniform Estimates for Regularization of Free Boundary Problems, Analysis and Partial Differential Equations, C. SADOSKY Ed., Marcel DECKER, 1990, pp. 567-619. Zbl0702.35252MR1044809
3. [3] H. Berestycki and L. Nirenberg, Asymptotic Behaviour via the Harnack Inequality, Nonlinear Analysis, a Tribute in Honor of Giovanni Prodi, Scuola Normale Superiore, Pisa, 1991, pp. 135-144. Zbl0840.35011MR1205378
4. [4] H. Brezis and L. Oswald, Singular Solutions for Some Semilinear Equations, Archive. Rational Mech. Anal., Vol. 99, 1987, pp. 249-259. Zbl0635.35035MR888452
5. [5] H. Brezis and L. Veron , Removable Singularities for Some Nonlinear Elliptic Equations, Archive. Rational Mech. Anal., Vol. 75, 1980, pp. 1-6. Zbl0459.35032MR592099
6. [6] L. Caffarelli, E.B. Fabes, S. Mortola and S. Salsa, Boundary Behavior of Nonnegative Solutions of Elliptic Operators in Divergence Form, Indiana Univ. Math. J., Vol. 30, 1981, pp. 621-640. Zbl0512.35038MR620271
7. [7] Yu.V. Egorov and M.A. Shubin (eds.), Partial Differential Equations III, Encyclopedia of Mathematical Sciences, Vol. 32, Springer-Verlag, Berlin, 1991. Zbl0741.00025MR1133472
8. [8] D. Gilbarg and J. Serrin, On Isolated Singularities of Solutions of Second Order Elliptic Differential equations, J. Analyse Math., Vol. 4, 1956, pp. 309-340. Zbl0071.09701MR81416
9. [9] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag, Berlin, 1983. Zbl0562.35001MR737190
10. [10] H. Imai, Picard Principle for Linear Elliptic Differential Operators, Hiroshima Math. J., Vol. 14, 1984, pp. 527-535. Zbl0571.35026MR772983
11. [11] Ju.T. Kuz'menko, Martin's Boundary for Elliptic Operators in Rn, Izv. Vysš. Učebn. Zaved. Matematika, Vol. 8, 1980, pp. 39-45 (Russian). Zbl0455.35043
12. [12] E.M. Landis and N.S. Nadirashvili, Positive Solutions of Second Order Elliptic Equations in Unbounded Domains, Math. USSR Sbornik, Vol. 54, 1986, pp. 129-134. Zbl0621.35038
13. [13] M. Murata, Isolated Singularities and Positive Solutions of Elliptic Equations in Rn, Proc. Japan Acad., Vol. 63, Ser. A, 1987, pp. 146-148. Zbl0652.35026MR906979
14. [14] M. Murata, Structure of Positive Solutions to (-Δ+V)u=0 in Rn, Duke Math. J., Vol. 53, 1986, pp. 869-943. Zbl0624.35023MR874676
15. [15] M. Murata, On construction of Martin Boundaries for Second Order Elliptic Equations, Publ. RIMS, Kyoto Univ., Vol. 26, 1990, pp. 585-627. Zbl0726.31009MR1081506
16. [16] M. Nakai, Martin Boundary Over an Isolated Singularity of Rotation Free Density, J. Math. Soc. Japan, Vol. 26, 1974, pp. 483-507. Zbl0281.30012MR361119
17. [17] M. Nakai, Picard Principle and Riemann Theorem, Tôhoku Math. J. Second Ser., Vol. 28, 1976, pp. 277-292. Zbl0335.35036MR409857
18. [18] Y. Pinchover, On Positive Solutions of Second-Order Elliptic Equations, Stability Results and Classification, Duke Math. J., Vol. 57, 1988, pp. 955-980. Zbl0685.35035MR975130
19. [19] Y. Pinchover, On the Equivalence of Green Functions of Second Order Elliptic Equations in Rn, Differential and Integral Equations, Vol. 5, 1992, pp. 481-493. Zbl0772.35015MR1157482
20. [20] R.G. Pinsky, A Probabilistic Approach to a Theorem of Gilbarg and Serrin, Israel J. Math., Vol. 74, 1991, pp. 1-12. Zbl0756.35021MR1135225
21. [21] R.G. Pinsky, A New Approach to the Martin Boundary via Diffusions Conditioned to Hit a Compact Set, Ann. Prob., 1993. Zbl0777.60075MR1207233
22. [22] J. Serrin, Local Behaviour of Solutions of Quasilinear Equations, Acta Math., Vol. 111, 1964, pp. 247-302. Zbl0128.09101MR170096
23. [23] J. Serrin, Isolated Singularities of Solutions of Quasilinear Equations, Acta Math., Vol. 113, 1965, pp. 219-240. Zbl0173.39202MR176219
24. [24] J. Serrin and H.F. Weinberger, Isolated Singularities of Solutions of Linear Elliptic Equations, Amer. J. Math., Vol. 88, 1966, pp. 258-272. Zbl0137.07001MR201815
25. [25] J.C. Taylor, On the Martin Compactification of a Bounded Lipschitz Domain in a Riemannian Manifold, Ann. Inst. Fourier, Vol. 28, 1978, pp. 25-52. Zbl0363.31010MR486580
26. [26] J.L. Vazquez and C. Yarur, Schrödinger Equations with Unique Positive Isolated Singularities, Manuscripta Math., Vol. 67, 1990, pp. 143-163. Zbl0723.35025MR1042235
27. [27] L. Véron, Limit Behaviour of Singular Solutions of Some Semilinear Elliptic Equations, Partial Differential Equations, Banach Center Publications, Vol. 19, PWN-Polish Scientific Publishers, Warsaw, 1987, pp. 311-350. Zbl0661.35027MR1055181
28. [28] C.S. Yarur, Isolated Singularities for Sublinear Elliptic Equations, Comm. Partial Differential Equations, Vol. 15, 1990, pp. 1361-1379. Zbl0726.35042MR1077470
29. [29] Z. Zhao, Subcriticality and gaugeability of the Schrödinger Operator, Trans. Amer. Math. Soc., Vol. 334, 1992, pp. 75-96. Zbl0765.60063MR1068934

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