PUBLICATIONS
by
Krzysztof P. Rybakowski

  1. (with M. Carbinatto) On convergence and compactness in parabolic problems with globally large diffusion and nonlinear boundary conditions, Topological Methods in Nonl. Analysis, to appear.
  2. On curved squeezing and Conley index, Topological Methods in Nonl. Analysis, 38(2011), 207-232.
  3. (with M. Carbinatto), Localized singularities and the Conley index, Topological Methods in Nonl. Analysis, 37(2011), 1-36.
  4. (with M. Carbinatto), Conley index and homology index braids in singular perturbation problems without uniqueness of solutions, Topological Methods in Nonl. Analysis, 35(2010), 1-32.
  5. (with A. Cwiszewski), Singular dynamics of the strongly damped beam equation, Journal of Differential Equations, 247(2009), 3202-3233.
  6. (with M. Carbinatto), On the suspension isomorphism for index braids in a singular perturbation problem, Topological Methods in Nonl. Analysis, 32(2008), 199-226.
  7. (with M. Prizzi), Attractors for singularly perturbed semilinear damped wave equations on unbounded domains, Topological Methods in Nonl. Analysis, 32 (2008), 1-20.
  8. (with M. Prizzi), Attractors for semilinear damped wave equations on arbitrary unbounded domains, Topological Methods in Nonl. Analysis, 31 (2008), 49-82.
  9. (with M. Prizzi), Attractors for reaction-diffusion equations on arbitrary unbounded domains, Topological Methods in Nonl. Analysis, 30 (2007), 251-270.
  10. (with M. Carbinatto), Continuation of the connection matrix for singularly perturbed hyperbolic equations, Fund. Math., 196 (2007), 253-273.
  11. The suspension isomorphism for cohomology index braids, Topological Methods in Nonl. Analysis, 29 (2007), 1-28.
  12. (with M. Carbinatto), The suspension isomorphism for homology index braids, Topological Methods in Nonl. Analysis, 28 (2006), 199-233.
  13. (with M. Carbinatto), Homology braids and infinite-dimensional Conley index theory, Topological Methods in Nonl. Analysis, 26 (2005), 35-74.
  14. (with M. Carbinatto), Continuation of the connection matrix in singular perturbation problems, Ergodic Theory and Dynamical Systems, 26 (2006), 1021-1059.
  15. (with M. Carbinatto), Nested index filtrations and continuation of the connection matrix, J. Differential Equations 207 (2004), 458-488.
  16. Conley index and singularly perturbed hyperbolic equations, Topological Methods in Nonl. Analysis 22 (2003), 203-244.
  17. (with M. Carbinatto), Morse-decompositions in the absence of uniqueness, II, Topological Methods in Nonl. Analysis 21 (2003), 17-53.
  18. (with M. Izydorek), Multiple solutions of strongly indefinite elliptic systems via a Galerkin-type Conley index theory, Fund. Math. 176 (2003 ), 233-249.
  19. An Introduction to the Conley Index in Noncompact Spaces, appendix to ``Dynamics in Infinite Dimensions'', by J. Hale et al., Appl. Math. Sciences, Vol. 47, 2nd edition, Springer Verlag, New York, 2002, 241-266.
  20. (with M. Izydorek), The Conley index in Hilbert spaces and a problem of Angenent and van der Vorst, Fund. Math. 173(2002), 77-100.
  21. (with M. Izydorek), On the Conley index in Hilbert spaces in the absence of uniqueness, Fund. Math. 171(2002), 31-52.
  22. (with M. Carbinatto), Morse-decompositions in the absence of uniqueness, Topological Methods in Nonl. Analysis 18(2001), 205-242.
  23. (with M. Carbinatto), On convergence, admissibility and attractors for damped wave equations on squeezed domains, Proc. A, Royal Soc. Edinburgh 132A(2002), 765-791.
  24. (with M. Carbinatto), On a general Conley index continuation principle for singular perturbation problems, Ergodic Theory and Dynamical Systems 22(2002), 729-755.
  25. (with M. Carbinatto), Conley index continuation and thin domain problems, Topological Methods in Nonl. Analysis 16 (2000), 201-251.
  26. (with M. Prizzi), Recent results on thin domain problems II, Topological Methods in Nonl. Analysis 19(2002), 199-219.
  27. (with M. Prizzi), On inertial manifolds for reaction-diffusion equations on genuinely high-dimensional thin domains, Studia Math. 154 (2003), 253-275.
  28. (with M. Prizzi and M. Rinaldi) Curved thin domains and parabolic equations, Studia Math. 151(2002), 109-140.
  29. (with M. Prizzi) The effect of domain squeezing upon the dynamics of reaction-diffusion equations, J. Differential Equations 173 (2001), 271-320.
  30. (with M. Prizzi) Inertial manifolds on squeezed domains, J. Dynamics and Differential Equations 15 (2003), 1-48.
  31. (with M. Prizzi) Some recent results on thin domain problems, Topological Methods in Nonl. Analysis 14 (1999), 239-255.
  32. (with M. Prizzi) Dynamics on thin domains, in: International Conference on Differential Equations, Berlin 1999, World Scientific, 2000, 753-759.
  33. (with M. Rinaldi) Some remarks on tubular neighborhoods and gluing in Morse-Floer homology, Banach Center Publications 47 (1999), 233-246.
  34. (with M. Prizzi) Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains, J. Differential Equations 142 (1998), 17-53.
  35. (with M. Prizzi) Complicated dynamics of parabolic equations with simple gradient dependence, Trans. Amer. Math. Soc. 350 (1998), 3119-3130.
  36. (with M. Prizzi) Some recent results on chaotic dynamics of differential equations, Univ. Jagiellonicae Acta Mathematica XXXVI (1998), 231-235.
  37. The center manifold technique and complex dynamics of parabolic equations, in: Topological Methods in Differential Equations and Inclusions (A. Granas, M. Frigon, eds.), NATO ASI Series 472, Kluwer Academic, 1995, 411-446.
  38. (with P. Polacik) Imbedding vector fields in scalar parabolic Dirichlet BVPs, Annali Scuola Norm. Superiore Pisa XXI (1995), 737-749.
  39. (with P. Polacik) Nonconvergent bounded trajectories in semilinear heat equations, J. Differential Equations 124 (1995), 472-494.
  40. Realization of arbitrary vector fields on invariant manifolds of delay equations, J. Differential Equations 114 (1994), 222-231.
  41. Realization of arbitrary vector fields on center manifolds of parabolic equations, J. Differential Equations 114 (1994), 199-221.
  42. On proving existence and smoothness of invariant manifolds in singular perturbation problems, Topological Methods in Nonl. Analysis 2 (1993), 21-34.
  43. An abstract approach to smoothness of invariant manifolds, Applicable Analysis 49 (1993) 119-150.
  44. (with M. Mrozek) Discretized ODEs and the Conley Index, J. of Dynamics and Differential Equations 4 (1992) 57-63.
  45. (with G. Caristi and T. Wessolek) Persistence and spatial patterns in a one-predator-two-prey Lotka-Volterra model with diffusion, Annali Mat. Pura ed Appl.(IV) CLXI (1992), 345-377.
  46. An abstract fixed-point theorem of Vanderbauwhede-Van Gils type, in: ``The Mathematical Heritage of C.F. Gauss - Geometry, Topology and Number Theory'', G.M.Rassias, ed., World Scientific Publ. Co., 1991, 645-651.
  47. (with M. Mrozek) Nontrivial full bounded solutions of time-periodic semilinear parabolic PDEs, Proc. Royal Soc. Edinburgh 117A (1991), 305-315.
  48. Formulas for higher-order Fréchet derivatives of composite maps, implicitly defined maps and solutions of differential equations, Nonlinear Analysis, TMA 16 (1991), 517-532.
  49. Formulas for higher-order finite expansions of composite maps, in: ``The Mathematical Heritage of C.F. Gauss - Geometry, Topology and Number Theory'', G.M.Rassias, ed., World Scientific Publ. Co., 1991, 652-669.
  50. (with M. Mrozek) A cohomological Conley index for maps on metric spaces, J. Differential Equations 90 (1991), 143-171.
  51. The Homotopy Index and Partial Differential Equations, Universitext, Springer Verlag, Berlin, Heidelberg, New York, 1987, 208 pages.
  52. (with J. Mawhin) On continuation theorems for semilinear equations in Banach spaces: a survey, ``Nonlinear functional analysis and fixed point theory'', G.M.Rassias, ed., World Scientific Publ. Co., 1987, 367-405.
  53. On critical groups and the homotopy index in Morse theory on Hilbert manifolds, Rend. Ist. Matem. Univ. Trieste, Vol. XVIII (1986), 163-176.
  54. Some recent results in the homotopy index theory in infinite dimensions, Rend. Ist. Matem. Univ. Trieste, Vol. XVIII (1986), 83-92.
  55. (with S. Dunbar and K. Schmitt) Persistence in models of predator-prey populations with diffusion, J. Differential Equations 65 (1986), 117-138.
  56. A homotopy index continuation method and periodic solutions of second order gradient systems, J. Differential Equations 65 (1986), 203-218.
  57. On a relation between the Brouwer degree and the Conley index for gradient flows, Bull. Soc. Math. Belg., série B, Vol. 37, fasc. II (1985), 87-96.
  58. (with S. Kuen) Boundedness of solutions of a system of integrodifferential equations, J. Math. Anal. Appl., Vol. 112 (1985), 378-390.
  59. Nontrivial solutions of elliptic boundary value problems with resonance at zero, Annali Mat. Pura ed Appl. (IV), Vol. CXXXIX (1985), 237-278.
  60. An index product-formula for the study of elliptic resonance problems, J. Differential Equations 56 (1985), 408-425.
  61. (with E. Zehnder) On a Morse equation in Conley's index theory for semiflows on metric spaces, Ergodic Theory and Dynamical Systems, 5 (1985), 123-143.
  62. Irreducible invariant sets and asymptotically linear functional differential equations, Boll. Unione Mat. Italiana (6) 3-B (1984), 245-271.
  63. Trajectories joining critical points of nonlinear parabolic and hyperbolic partial differential equations, J. Differential Equations 51 (1984), 182-212.
  64. An Introduction to the Homotopy Index on Noncompact Spaces, appendix to ``An Introduction to Infinite-dimensional Dynamical Systems - Geometric Theory'', by J. Hale et al., Appl. Math. Sciences, Vol. 47, Springer Verlag, New York, 1983, 147-191.
  65. (with J. Hale) On a gradient-like integro-differential equation, Proc. Royal Soc. Edinburgh, 92A (1982), 77-85.
  66. The Morse index, repeller-attractor pairs and the connection index for semiflows on noncompact spaces, J. Differential Equations 47 (1983), 66-98.
  67. On the Morse index for infinite-dimensional semiflows, Dynamical Systems II (Bednarek/Cesari, eds.), Acad. Press (1982), 633-637.
  68. On the homotopy index for infinite-dimensional semiflows, Trans. Amer. Math. Soc. 269 (1982), 351-382.
  69. Some remarks on periodic solutions of Carathéodory RFDEs via Wazewski's principle, Riv. Mat. Univ. Parma (4) 8, (1982), 377-385.
  70. A topological principle for retarded functional differential equations, J. Differential Equations 39 (1981), 131-150.
  71. Wazewski's principle for retarded functional differential equations, J. Differential Equations 36 (1980), 117-138.
  72. On Wazewski's principle for retarded functional differential equations, Ph.D. Dissertation, Brown University, June 1979.

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