46 citations · 176 across the 42 of their papers we have counts for
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Global existence in infinite lattices of nonlinear oscillators: The Discrete Klein-Gordon equation
Nikos I. Karachalios
Pointing out the difference between the Discrete Nonlinear Schrödinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the s…
Global Existence and Compact Attractors for the Discrete Nonlinear Schrödinger equation
Nikos I. Karachalios, Athanasios N. Yannacopoulos
We study the asymptotic behavior of solutions of discrete nonlinear Schrödinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the…
Asymptotic Behavior of Solutions of Complex Discrete Evolution Equations: The Discrete Ginzburg-Landau Equation
Nikos I. Karachalios, Hector E. Nistazakis, Athanasios N. Yannacopoulos
We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dyna…
A remark on the existence of breather solutions for the Discrete Nonlinear Schrödinger Equation in infinite lattices: The case of site dependent anharmonic parameter
Nikos I. Karachalios
We discuss the existence of breather solutions for a Discrete Nonlinear Schrödinger equation in an infinite -dimensional lattice, involving site dependent anharmonic parameter.…
On the Dynamics of a Degenerate Parabolic Equation: Global Bifurcation of Stationary States and Convergence
Nikos I. Karachalios, Nikos B. Zographopoulos
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points or be unbounded. We show the e…