Generalized vector equilibrium-like problems without pseudomonotonicity in Banach spaces.
Générateur des semi-groupes non linéaires et la formule de Lie-Trotter
Generation of nonlinear semigroups by a partial differential equation.
Generation theory for semigroups of holomorphic mappings in Banach spaces.
Generic convergence of iterates for a class of nonlinear mappings.
Generic differentiability of mappings and convex functions in Banach and locally convex spaces
Geometric properties of Banach spaces and metric fixed point theory.
Geometric properties related to the fixed point property in Banach spaces.
Geometry of some simple nonlinear differential operators
Global asymptotic stability of inhomogeneous iterates.
Global bounds for cocoercive variational inequalities.
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
Global existence for a semilinear prabolic Volterra equation.
Global existence for coupled Klein-Gordon equations with different speeds
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.
Global existence for the Hamilton-Jacobi equations in Hilbert space
Global existence, uniqueness, and continuous dependence for a reaction-diffusion equation with memory.
Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.
Global stability of delayed Hopfield neural networks under dynamical thresholds.
Gradient maps and boundedness of Gâteaux differentials
Gradient systems of closed operators
A classical result on the existence of global attractors for gradient systems is extended to the case of a semigroup S(t) lacking strong continuity, but satisfying the weaker property of being a closed map for every fixed t ≥ 0.