Selected Publications on spectral theory for nonautonomous/random evolution operators

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Nonlocal dispersal equations with almost periodic dependence. I. Principal spectral theory (with Maria Amarakristi Onyido) (Pdf )

Criteria for the Existence of Principal Eigenvalues of Time Periodic Cooperative Linear Systems with Nonlocal Dispersal (with Xiongxiong Bao) ( Pdf )

Spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications (with Xiaoxia Xie) ( Pdf )

Formulas for generalized principal Lyapunov exponent for parabolic PDEs (with Janusz Mierczynski) (Pdf )

Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems (with Janusz Mierczynski) (Pdf )

Approximations of Random Dispersal Operators/Equations by Nonlocal Dispersal Operators/Equations (with Xiaoxia Xia)) (Pdf )

On Principal Spectrum Points/Principal Eigenvalues of Nonlocal Dispersal Operators and Applications (with Xiaoxia Xie) (Pdf )

Criteria for the Existence and Lower Bounds of Principal Eigenvalues of Time Periodic Nonlocal Dispersal Operators and Applications (with Nar Rawal), Journal of Dynamics and Differential Equations , 24 (2012), 927-954. ( Abstract)

Principal Lyapunov Exponents and Principal Floquet Spaces of Positive Random Dynamical Systems. II. Finite-dimensional Systems (with Janusz Mierczynski), Journal of Mathematical Analysis and Applications ( Abstract)

Principal Lyapunov Exponents and Principal Floquet Spaces of Positive Random Dynamical Systems. I. General Theory (with Janusz Mierczynski), Transactions of the American Mathematical Society, ( Abstract)

Effects of Spatial Variations and Dispersal Strategies on Principal Eigenvalues of Dispersal Operators and Spreading Speeds of Monostable Equations (with Georg Hetzer and Aijun Zhang), The Rocky Mountain Journal of Mathematics, ( Abstract)

Spectral Theory for Forward Nonautonomous Parabolic Equations and Applications (with J. Mierczynski), The Fields Institute Communication Series, 64 (2013), 57-99 ( Abstract)

Persistence in Forward Nonautonomous Systems of Parabolic Equations (with J. Mierczynski), Journal of Dynamics and Differential Equations, 23 (2011), 551-571.

Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications (with J. Mierczynski), Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics Series, edited by Brezis, Douglas and Jeffrey, CRC Press (2008) ( Monograph)

Time averaging for nonautonomous/random linear parabolic equations (with J. Mierczynski}, Discrete and Continuous Dynamical Systems `Series B, 9 (2008), 661-699.

Spectral Theory for General Nonautonomous/Random Dispersal Evolution Operators (with G.T. Vickers), J. Differential Equations , 235 (2007), 262--297.

Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence (with V. Hutson and G. T. Vickers), Rocky Mountain Journal of Mathematics , 38 (2008), 1147-1175.

The Faber-Krahn inequality for random/nonautonomous parabolic equations (with J. Mierczynski), Communications on Pure and Applied Analysis , 4 (2005),101-114.

Lyapunov Exponents and Asymptotic Dynamics in Random Kolmogorov Models (with J. Mierczynski), Journal of Evolution Equations , 4 (2004), 371-390.

Exponential Separation and Principal Lyapunov Exponent/Spectrum for Random/Nonautonomous Parabolic
Equations (with J. Mierczynski), Journal of Differential Equations, 191 (2003), 175-205.

Estimates for the Principle Spectrum Point for Certain Parabolic Operators (with V. Hutson and G.T. Vickers), Proceedings of the American Mathematical Society, 129 (2001), 1669-1679.