A condition on delay for differential equations with discrete state-dependent delay

Abstract

Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent delay: uniqueness and well-posedness in the space of continuous functions, Nonlinear Analysis: Theory, Methods and Applications, 70 (11) (2009), 3978-3986] is developed. We propose and study a state-dependent analogue of the condition which is sufficient for the well-posedness of the corresponding initial value problem on the whole space of continuous functions $C$. The dynamical system is constructed in $C$ and the existence of a compact global attractor is proved.

Cited by in corpus (7)

• Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold
• Dynamics of second order in time evolution equations with state-dependent delay
• Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
• Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses
• Viral infection model with diffusion and state-dependent delay: stability of classical solutions
• Theory of well-posedness for delay differential equations via prolongations and $C^1$-prolongations: its application to state-dependent delay
• Global Dynamics of a Predator-Prey Model with State-Dependent Maturation-Delay