@article{AIHPC_2007__24_5_711_0, author = {H\'uska, Juraj and Pol\'a\v{c}ik, Peter and Safonov, Mikhail V.}, title = {Harnack inequalities, exponential separation, and perturbations of principal {Floquet} bundles for linear parabolic equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {711--739}, publisher = {Elsevier}, volume = {24}, number = {5}, year = {2007}, doi = {10.1016/j.anihpc.2006.04.006}, mrnumber = {2348049}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.04.006/} }
TY - JOUR AU - Húska, Juraj AU - Poláčik, Peter AU - Safonov, Mikhail V. TI - Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2007 SP - 711 EP - 739 VL - 24 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2006.04.006/ DO - 10.1016/j.anihpc.2006.04.006 LA - en ID - AIHPC_2007__24_5_711_0 ER -
%0 Journal Article %A Húska, Juraj %A Poláčik, Peter %A Safonov, Mikhail V. %T Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations %J Annales de l'I.H.P. Analyse non linéaire %D 2007 %P 711-739 %V 24 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2006.04.006/ %R 10.1016/j.anihpc.2006.04.006 %G en %F AIHPC_2007__24_5_711_0
Húska, Juraj; Poláčik, Peter; Safonov, Mikhail V. Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations. Annales de l'I.H.P. Analyse non linéaire, Volume 24 (2007) no. 5, pp. 711-739. doi : 10.1016/j.anihpc.2006.04.006. http://www.numdam.org/articles/10.1016/j.anihpc.2006.04.006/
[1] Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa 22 (1968) 607-694. | Numdam | MR | Zbl
,[2] Elliptic equations, principal eigenvalue and dependence on the domain, Comm. Partial Differential Equations 21 (1996) 971-991. | MR | Zbl
,[3] The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math. 47 (1994) 47-92. | MR | Zbl
, , ,[4] Hopf's lemma and anti-maximum principle in general domains, J. Differential Equations 119 (2) (1995) 450-472. | MR | Zbl
,[5] Floquet bundles for scalar parabolic equations, Arch. Rational Mech. Anal. 129 (1995) 245-304. | MR | Zbl
, , ,[6] Dirichlet problems on varying domains, J. Differential Equations 188 (2003) 591-624. | MR | Zbl
,[7] Domain perturbation for linear and nonlinear parabolic equations, J. Differential Equations 129 (1996) 358-402. | MR | Zbl
,[8] Existence and perturbation of principal eigenvalues for a periodic-parabolic problem, Electron. J. Differential Equations, Conf. 05 (2000) 51-67. | MR | Zbl
,[9] Heat kernel estimates for operators with boundary conditions, Math. Nachr. 217 (2000) 13-41. | MR | Zbl
,[10] Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 1998. | MR | Zbl
,[11] A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations, Illinois J. Math. 30 (1986) 536-565. | MR | Zbl
, , ,[12] Behavior near the boundary of positive solutions of second order parabolic equations, J. Fourier Anal. Appl. 3 (1997) 871-882. | MR | Zbl
, ,[13] Behavior near the boundary of positive solutions of second order parabolic equations II, Trans. Amer. Math. Soc. 12 (1999) 4947-4961. | MR | Zbl
, , ,[14] Growth theorems and Harnack inequality for second order parabolic equations, in: Harmonic Analysis and Boundary Value Problems, Contemp. Math., vol. 277, Amer. Math. Soc., Providence, RI, 2001, pp. 87-112. | MR | Zbl
, ,[15] Second order parabolic equations in nonvariational form: boundary Harnack principle and comparison theorems for nonnegative solutions, Ann. Mat. Pura Appl. 138 (1984) 267-296. | MR | Zbl
,[16] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer, New York, 1981. | MR | Zbl
,[17] Periodic-Parabolic Boundary Value Problems and Positivity, Longman Scientific & Technical, Harlow, 1991. | MR | Zbl
,[18] Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems, SIAM J. Math. Anal. 24 (1993) 1312-1330. | MR | Zbl
, ,[19] Harnack inequality and exponential separation for oblique derivative problems on Lipschitz domains, J. Differential Equations 226 (2006) 541-557. | MR | Zbl
,[20] The principal Floquet bundle and exponential separation for linear parabolic equations, J. Dynam. Differential Equations 24 (2004) 1312-1330. | MR | Zbl
, ,[21] J. Húska, P. Poláčik, M.V. Safonov, Principal eigenvalues, spectral gaps and exponential separation between positive and sign-changing solutions of parabolic equations, in: Disc. Cont. Dynamical Systems, Supplement, Proceedings of the 5th International Conference on Dynamical Systems and Differential Equations, Pomona 2004, 2005, pp. 427-435.
[22] Estimates for the principal spectrum point for certain time-dependent parabolic operators, Proc. Amer. Math. Soc. 129 (6) (2001) 1669-1679, (electronic). | MR | Zbl
, , ,[23] A property of the solutions of parabolic equations with measurable coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1) (1980) 161-175. | MR | Zbl
, ,[24] Linear and Quasilinear Equations of Parabolic Type, Translation of Mathematical Monographs, American Mathematical Society, Providence, RI, 1968. | Zbl
, , ,[25] Second Order Equations of Elliptic and Parabolic Type, Translation of Mathematical Monographs, American Mathematical Society, Providence, RI, 1998. | MR | Zbl
,[26] Second Order Parabolic Differential Equations, World Scientific Publishing Co. Inc., River Edge, NJ, 1996. | MR | Zbl
,[27] J. Mierczyński, Flows on order bundles, unpublished.
[28] p-arcs in strongly monotone discrete-time dynamical systems, Differential Integral Equations 7 (1994) 1473-1494. | MR | Zbl
,[29] Globally positive solutions of linear PDEs of second order with Robin boundary conditions, J. Math. Anal. Appl. 209 (1997) 47-59. | MR | Zbl
,[30] Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions, J. Math. Anal. Appl. 226 (1998) 326-347. | MR | Zbl
,[31] The principal spectrum for linear nonautonomous parabolic pdes of second order: Basic properties, J. Differential Equations 168 (2000) 453-476. | MR | Zbl
,[32] Exponential separation and principal Lyapunov exponent/spectrum for random/nonautonomous parabolic equations, J. Differential Equations 191 (2003) 175-205. | MR | Zbl
, ,[33] A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964) 101-134, Correction in, Comm. Pure Appl. Math. 20 (1967) 231-236. | MR | Zbl
,[34] The uniqueness of positive solutions of parabolic equations of divergence form on an unbounded domain, Nagoya Math. J. 130 (1993) 111-121. | MR | Zbl
,[35] Parabolic equations: asymptotic behavior and dynamics on invariant manifolds, in: (Ed.), Handbook on Dynamical Systems, vol. 2, Elsevier, Amsterdam, 2002, pp. 835-883. | MR | Zbl
,[36] On uniqueness of positive entire solutions and other properties of linear parabolic equations, Discrete Contin. Dynamical Systems 12 (2005) 13-26. | MR | Zbl
,[37] Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems, Arch. Rational Mech. Anal. 116 (1992) 339-360. | MR | Zbl
, ,[38] Exponential separation and invariant bundles for maps in ordered Banach spaces with applications to parabolic equations, J. Dynamics Differential Equations 5 (1993) 279-303, Erratum, J. Dynamics Differential Equations 6 (1) (1994) 245-246. | MR | Zbl
, ,[39] Analycity properties of the characteristic exponents of random matrix products, Adv. in Math. 32 (1979) 68-80. | MR | Zbl
,[40] Almost automorphic and almost periodic dynamics in skew-product semiflows, Mem. Amer. Math. Soc. 647 (1998) 93. | MR | Zbl
, ,[41] I. Tereščák, Dynamics of smooth strongly monotone discrete-time dynamical systems, Preprint.
[42] I. Tereščák, Dynamical systems with discrete Lyapunov functionals, PhD thesis, Comenius University, 1994.
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