PUBLICATIONS
by
Krzysztof P. Rybakowski
- Curved squeezing of unbounded domains and attractors, in preparation.
- (with M. Carbinatto) Homology index braids and tubular
neighborhoods, in preparation.
- Curved squeezing of unbounded domains and tail
estimates, Topological Methods in Nonl. Analysis, to appear.
- (with M. Carbinatto) Morse decompositions and tubular
neighborhoods, Ergodic Theory and Dynamical Systems, to appear.
- (with M. Carbinatto) Resolvent convergence for Laplace
operators on unbounded curved squeezed domains, Topological
Methods in Nonl. Analysis, 42 (2013), 233-257.
- (with M. Carbinatto) Conley index and tubular
neighborhoods, J. Differential Equations 254 (2013), 933-959.
- A note on Ważewski principle and Conley index,
Invited Paper, Sixth European Congress of Mathematics, Wiadomości
Matematyczne 48 (2012), 223-238.
- (with M. Carbinatto) On convergence and compactness in
parabolic problems with globally large diffusion and nonlinear
boundary conditions, Topological Methods in Nonl. Analysis, 40
(2012), 1-28.
- On curved squeezing and Conley index, Topological
Methods in Nonl. Analysis, 38 (2011), 207-232.
- (with M. Carbinatto), Localized singularities and the
Conley index, Topological Methods in Nonl. Analysis, 37 (2011),
1-36.
- (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.
- (with A. Cwiszewski), Singular dynamics of the
strongly damped beam equation, Journal of Differential Equations,
247 (2009), 3202-3233.
- (with M. Carbinatto), On the suspension isomorphism
for index braids in a singular perturbation problem, Topological
Methods in Nonl. Analysis, 32 (2008), 199-226.
- (with M. Prizzi), Attractors for singularly perturbed
semilinear damped wave equations on unbounded domains,
Topological Methods in Nonl. Analysis, 32 (2008), 1-20.
- (with M. Prizzi), Attractors for semilinear damped
wave equations on arbitrary unbounded domains, Topological
Methods in Nonl. Analysis, 31 (2008), 49-82.
- (with M. Prizzi), Attractors for reaction-diffusion
equations on arbitrary unbounded domains, Topological Methods in
Nonl. Analysis, 30 (2007), 251-270.
- (with M. Carbinatto), Continuation of the connection
matrix for singularly perturbed hyperbolic equations, Fund.
Math., 196 (2007), 253-273.
- The suspension isomorphism for cohomology index
braids, Topological Methods in Nonl. Analysis, 29 (2007), 1-28.
- (with M. Carbinatto), The suspension isomorphism for
homology index braids, Topological Methods in Nonl. Analysis, 28
(2006), 199-233.
- (with M. Carbinatto), Homology braids and
infinite-dimensional Conley index theory, Topological Methods in
Nonl. Analysis, 26 (2005), 35-74.
- (with M. Carbinatto), Continuation of the connection
matrix in singular perturbation problems, Ergodic Theory and
Dynamical Systems, 26 (2006), 1021-1059.
- (with M. Carbinatto), Nested index filtrations and
continuation of the connection matrix, J. Differential Equations
207 (2004), 458-488.
- Conley index and singularly perturbed hyperbolic
equations, Topological Methods in Nonl. Analysis 22 (2003),
203-244.
- (with M. Carbinatto), Morse-decompositions in the
absence of uniqueness, II, Topological Methods in Nonl. Analysis
21 (2003), 17-53.
- (with M. Izydorek), Multiple solutions of strongly
indefinite elliptic systems via a Galerkin-type Conley index theory,
Fund. Math. 176 (2003 ), 233-249.
- 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.
- (with M. Izydorek), The Conley index in Hilbert
spaces and a problem of Angenent and van der Vorst, Fund. Math.
173(2002), 77-100.
- (with M. Izydorek), On the Conley index in Hilbert
spaces in the absence of uniqueness, Fund. Math. 171(2002), 31-52.
- (with M. Carbinatto), Morse-decompositions in the
absence of uniqueness, Topological Methods in Nonl. Analysis
18(2001), 205-242.
- (with M. Carbinatto), On convergence, admissibility
and attractors for damped wave equations on squeezed domains,
Proc. A, Royal Soc. Edinburgh 132A(2002), 765-791.
- (with M. Carbinatto), On a general Conley index
continuation principle for singular perturbation problems, Ergodic
Theory and Dynamical Systems 22(2002), 729-755.
- (with M. Carbinatto), Conley index continuation and
thin domain problems, Topological Methods in Nonl. Analysis 16
(2000), 201-251.
- (with M. Prizzi), Recent results on thin domain
problems II, Topological Methods in Nonl. Analysis 19(2002),
199-219.
- (with M. Prizzi), On inertial manifolds for
reaction-diffusion equations on genuinely high-dimensional thin
domains, Studia Math. 154 (2003), 253-275.
- (with M. Prizzi and M. Rinaldi) Curved thin domains
and parabolic equations, Studia Math. 151(2002), 109-140.
- (with M. Prizzi) The effect of domain squeezing upon the
dynamics of reaction-diffusion equations, J. Differential
Equations 173 (2001), 271-320.
- (with M. Prizzi) Inertial manifolds on squeezed domains,
J. Dynamics and Differential Equations 15 (2003), 1-48.
- (with M. Prizzi) Some recent results on thin domain
problems, Topological Methods in Nonl. Analysis 14 (1999),
239-255.
- (with M. Prizzi) Dynamics on thin domains, in:
International Conference on Differential Equations, Berlin 1999, World
Scientific, 2000, 753-759.
- (with M. Rinaldi) Some remarks on tubular
neighborhoods and gluing in Morse-Floer homology, Banach Center
Publications 47 (1999), 233-246.
- (with M. Prizzi) Inverse problems and chaotic
dynamics of parabolic equations on arbitrary spatial domains, J.
Differential Equations 142 (1998), 17-53.
- (with M. Prizzi) Complicated dynamics of parabolic
equations with simple gradient dependence, Trans. Amer. Math. Soc.
350 (1998), 3119-3130.
- (with M. Prizzi) Some recent results on chaotic
dynamics of differential equations, Univ. Jagiellonicae Acta
Mathematica XXXVI (1998), 231-235.
- 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.
- (with P. Polacik) Imbedding vector fields in scalar
parabolic Dirichlet BVPs, Annali Scuola Norm. Superiore Pisa XXI
(1995), 737-749.
- (with P. Polacik) Nonconvergent bounded trajectories
in semilinear heat equations, J. Differential Equations 124
(1995), 472-494.
- Realization of arbitrary vector fields on invariant
manifolds of delay equations, J. Differential Equations 114
(1994), 222-231.
- Realization of arbitrary vector fields on center
manifolds of parabolic equations, J. Differential Equations 114
(1994), 199-221.
- On proving existence and smoothness of invariant
manifolds in singular perturbation problems, Topological Methods
in Nonl. Analysis 2 (1993), 21-34.
- An abstract approach to smoothness of invariant
manifolds, Applicable Analysis 49 (1993) 119-150.
- (with M. Mrozek) Discretized ODEs and the Conley Index,
J. of Dynamics and Differential Equations 4 (1992) 57-63.
- (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.
- 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.
- (with M. Mrozek) Nontrivial full bounded solutions of
time-periodic semilinear parabolic PDEs, Proc. Royal Soc.
Edinburgh 117A (1991), 305-315.
- Formulas for higher-order Fréchet derivatives of
composite maps, implicitly defined maps and solutions of differential
equations, Nonlinear Analysis, TMA 16 (1991), 517-532.
- 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.
- (with M. Mrozek) A cohomological Conley index for maps
on metric spaces, J. Differential Equations 90 (1991), 143-171.
- The Homotopy Index and Partial Differential Equations,
Universitext, Springer Verlag, Berlin, Heidelberg, New York, 1987, 208
pages.
- (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.
- On critical groups and the homotopy index in Morse
theory on Hilbert manifolds, Rend. Ist. Matem. Univ. Trieste, Vol.
XVIII (1986), 163-176.
- Some recent results in the homotopy index theory in
infinite dimensions, Rend. Ist. Matem. Univ. Trieste, Vol. XVIII
(1986), 83-92.
- (with S. Dunbar and K. Schmitt) Persistence in models
of predator-prey populations with diffusion, J. Differential
Equations 65 (1986), 117-138.
- A homotopy index continuation method and periodic
solutions of second order gradient systems, J. Differential
Equations 65 (1986), 203-218.
- 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.
- (with S. Kuen) Boundedness of solutions of a system of
integrodifferential equations, J. Math. Anal. Appl., Vol. 112
(1985), 378-390.
- Nontrivial solutions of elliptic boundary value
problems with resonance at zero, Annali Mat. Pura ed Appl. (IV),
Vol. CXXXIX (1985), 237-278.
- An index product-formula for the study of elliptic
resonance problems, J. Differential Equations 56 (1985), 408-425.
- (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.
- Irreducible invariant sets and asymptotically linear
functional differential equations, Boll. Unione Mat. Italiana (6)
3-B (1984), 245-271.
- Trajectories joining critical points of nonlinear
parabolic and hyperbolic partial differential equations, J.
Differential Equations 51 (1984), 182-212.
- 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.
- (with J. Hale) On a gradient-like integro-differential
equation, Proc. Royal Soc. Edinburgh, 92A (1982), 77-85.
- The Morse index, repeller-attractor pairs and the
connection index for semiflows on noncompact spaces, J.
Differential Equations 47 (1983), 66-98.
- On the Morse index for infinite-dimensional semiflows,
Dynamical Systems II (Bednarek/Cesari, eds.), Acad. Press (1982),
633-637.
- On the homotopy index for infinite-dimensional
semiflows, Trans. Amer. Math. Soc. 269 (1982), 351-382.
- Some remarks on periodic solutions of Carathéodory
RFDEs via Wazewski's principle, Riv. Mat. Univ. Parma (4) 8,
(1982), 377-385.
- A topological principle for retarded functional
differential equations, J. Differential Equations 39 (1981),
131-150.
- Wazewski's principle for retarded functional differential
equations, J. Differential Equations 36 (1980), 117-138.
- On Wazewski's principle for retarded functional
differential equations, Ph.D. Dissertation, Brown University, June
1979.
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