An existence result for nonlinear fractional differential equations on Banach spaces.
An existence theorem for bounded solutions of differential equations in Banach spaces
An existence theorem for differential inclusions on Banach space.
An interplay between the weak form of Peano's theorem and structural aspects of Banach spaces
We establish some results that concern the Cauchy-Peano problem in Banach spaces. We first prove that a Banach space contains a nontrivial separable quotient iff its dual admits a weak*-transfinite Schauder frame. We then use this to recover some previous results on quotient spaces. In particular, by applying a recent result of Hájek-Johanis, we find a new perspective for proving the failure of the weak form of Peano's theorem in general Banach spaces. Next, we study a kind of algebraic genericity...
An Lp-Analogue of the Weyl Alternative.
Application of Rothe's method to parabolic variational inequalities
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Applications of the Carathéodory theorem to PDEs
We discuss and exploit the Carathéodory theorem on existence and uniqueness of an absolutely continuous solution x: ℐ (⊂ ℝ) → X of a general ODE for the right-hand side ℱ : dom ℱ ( ⊂ ℝ × X) → X taking values in an arbitrary Banach space X, and a related result concerning an extension of x. We propose a definition of solvability of (*) admitting all connected ℐ and unifying the cases “dom ℱ is open” and “dom ℱ = ℐ × Ω for some Ω ⊂ X”. We show how to use the theorems mentioned above to get approximate...
Approximate inertial manifolds for nonlinear parabolic equations via steady-state determining mapping.
Approximate solutions for integrodifferential equations of the neutral type
The main objective of the present paper is to study the approximate solutions for integrodifferential equations of the neutral type with given initial condition. A variant of a certain fundamental integral inequality with explicit estimate is used to establish the results. The discrete analogues of the main results are also given.
Approximation of Hopf Bifurcation.
Approximation of solutions to evolution integrodifferential equations.
Approximations and error bounds for computing the inverse mapping
In this paper we propose a procedure to construct approximations of the inverse of a class of differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.
Approximations of solutions to nonlinear Sobolev type evolution equations.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects
In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations ü(t) + γ(t) + ∇ϕ(u(t)) + A(u(t)) = 0, where ∇ϕ is the gradient operator of a convex differentiable potential function ϕ: ,A: is a maximal monotone operator which is assumed to beλ-cocoercive, and γ > 0 is a damping parameter. Potential and non-potential effects are associated respectively to ∇ϕ and A. Under condition...
Asymptotic behavior of second-order dissipative evolution equations combining potential with non-potential effects*
In the setting of a real Hilbert space , we investigate the asymptotic behavior, as time t goes to infinity, of trajectories of second-order evolution equations ü(t) + γ(t) + ∇ϕ(u(t)) + A(u(t)) = 0, where ∇ϕ is the gradient operator of a convex differentiable potential function ϕ : , A : is a maximal monotone operator which is assumed to be λ-cocoercive, and γ > 0 is a damping parameter. Potential and non-potential effects are associated respectively to ∇ϕ and A. Under condition...
Asymptotic behavior of solutions of nonlinear functional differential equations.
Asymptotic behavior of weighted quadratic variation of bi-fractional Brownian motion
We prove, by means of Malliavin calculus, the convergence in of some properly renormalized weighted quadratic variations of bi-fractional Brownian motion (biFBM) with parameters and , when and .
Asymptotic behaviour of stochastic quasi dissipative systems
We prove uniqueness of the invariant measure and the exponential convergence to equilibrium for a stochastic dissipative system whose drift is perturbed by a bounded function.