Criteria of solvability for multidimensional Riccati equations

Arkiv for Matematik

Volumn 37, Issue 1, 1999, Pages 87-120

  Hansson, Kurt ^a   Maz'ya, Vladimir G ^a   Verbitsky, Igor E ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b UNIVERSITY OF MISSOURI   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010299468     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02384829     Document Type: Article

References (26)

1. ADAMS, D. R. and HEDBERG, L. I., Function Spaces and Potential Theory, Springer-Verlag, Berlin Heidelberg, 1996.
2. ADAMS, D. R. and PIERRE, M., Capacitary strong type estimates in semilinear problems, Ann. Inst. Fourier (Grenoble) 41:1 (1991), 117-135.
3. AGMON, S., On positlvity and decay of solutions of second order elliptic equations on Riemannian manifolds, in Methods of Functional Analysis and Theory of Elliptic Equations (Greco, D., ed.), pp. 19-52, Liguori, Naples, 1983.
4. n, J. London Math. Soc. 34 (1986), 274-290.
5. ANCONA, A., First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains, J. Anal. Math. 72 (1997), 45-92.
6. BARAS, P., Semilinear problem with convex nonlinearity, in Recent Advances in Nonlinear Elliptic and Parabolic Problems (Bénilan, P., Chípot, M., Evans, L. C. and Pierre, M., eds.), Pitman Research Notes in Math. Sciences 208, pp. 202-215, Longman, Harlow, 1989.
7. BARAS, P. and PIERRE, M., Singularités éliminables pour des équations semi-linéaires, Ann. Inst. Fourier (Grenoble) 34:1 (1984), 185-206.
8. CHUNG, K. L. and ZHAO, Z., From Brownian Motion to Schrödinger's Equation, Springer-Verlag, Berlin, 1995.
9. GRÜTER, M. and WIDMAN, K.-O., The Green function for uniformly elliptic equations, Manuscripta Math. 37 (1982), 303-342.
10. HANSSON, K., Imbedding theorems of Sobolev type in potential theory, Math. Scand. 45 (1979), 77-102.
11. HARTMAN, P., Ordinary Differential Equations, Republ. 2nd ed., Birkhäuser, Boston, Mass., 1982.
12. HAYMAN, W. K. and KENNEDY, P. B., Subharmonic Functions, Vol. 1, Academic Press, London New York San Francisco, 1976.
13. HEDBERG, L. I., On certain convolution inequalities, Proc. Amer. Math. Soc. 36 (1972), 505-510.
14. 1,1-domains, Ann. Inst. Fourier (Grenoble) 32:1 (1982), 105-117.
15. KALTON, N. J. and VERBITSKY, I. E., Nonlinear equations and weighted norm inequalities, to appear in Trans. Amer. Math. Soc.
16. LIONS, P. L., On the existence of positive solutions of semilinear elliptic equations, SIAM Rev. 24 (1982), 441-467.
17. MAZ'YA, V. G., On the theory of the n-dimensional Schrödinger operator, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1145-1172 (Russian).
18. MAZ'YA, V. G., Sobolev Spaces, Springer-Verlag, Berlin Heidelberg New York, 1985.
19. MAZ'YA, V. G. and VERBITSKY, I. E., Capacitary estimates for fractional integrals, with applications to partial differential equations and Sobolev multipliers, Ark. Mat. 33 (1995), 81-115.
20. NYSTRÖM, K., Integrability of Green potentials in fractal domains, Ark. Mat. 34 (1996), 335-381.
21. SCHECHTER, M., Hamiltonians for singular potentials, Indiana Univ. Math. J. 22 (1972), 483-503.
22. SIMON, B., Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526.
23. STEIN, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970.
24. VERBITSKY, I. E. and WHEEDEN, R. L., Weighted inequalities for fractional integrals and applications to semilinear equations, J. Funct. Anal. 129 (1995), 221-241.
25. WIDMAN, K.-O., Inequalities for the Green function and boundary continuity of the gradients of solutions of elliptic differential equations, Math. Scand. 21 (1967), 13-67.
26. ZHAO, Z., Green function for Schrödinger operator and conditioned Feynman-Kac gauge, J. Math. Anal. Appl. 116 (1986), 309-334.