Sergiu Aizicovici

Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints

Introduction Mathematical background Degree theoretic results Variational-hemivariational inequalities Hemivariational inequalities with an asymmetric subdifferential Bibliography.

On a class of second-order anti-periodic boundary value problems

Of concern is the existence and uniqueness of anti-periodic solutions to a class of abstract nonlinear second-order differential equations. The investigation relies on the theory of m-accretive operators in Banach or Hilbert spaces. Examples of boundary value problems for ordinary and partial differential equations are also discussed.

Anti-periodic solutions to a class of nonlinear differential equations in Hilbert space

Abstract A broad class of nonlinear, non-monotone anti-periodic boundary value problems in a Hilbert space is considered. As a preliminary step, the existence, uniqueness and continuous dependence upon data of anti-periodic solutions to some first- and second-order evolution equations associated to odd, noncoercive monotone operators is established. Applications of the theory to nonlinear partial differential equations are also discussed.

Nonlinear nonlocal Cauchy problems in Banach spaces

Abstract The aim of this paper is to study the existence of integral solutions for an abstract nonlinear Cauchy problem with nonlocal initial conditions. The approach relies on the use of the theory of nonlinear semigroups and Schauder’s fixed-point theorem.

Long-time stabilization of solutions to a phase-field model with memory

Abstract. We prove that any global bounded solution of a phase field model with memory terms tends to a single equilibrium state for large times. Because of the memory effects, the energy is not a Lyapunov function for the problem and the set of equilibria may contain a nontrivial continuum of stationary states. The method we develop is applicable to a more general class of equations containing memory terms.

Functional differential equations with nonlocal initial conditions.

We study the existence, uniqueness, asymptotic properties, and continuous dependence upon data of solutions to a class of abstract nonlocal Cauchy problems. The approach we use is based on the theory of m-accretive operators and related evolution equations in Banach spaces.

Existence and asymptotic results for a system of integro-partial differential equations

A non-Fourier phase field model is considered. A global existence result for a Dirichlet, or generalized Neumann, initial-boundary value problem is obtained, followed by a discussion of the regularity and asymptotic properties of solutions ast→∞.

Nodal solutions for

In this paper, we study a nonlinear elliptic equation driven by the sum of a p-Laplacian and a Laplacian ((p, 2)-equation), with a Caratheodory (p− 1)-(sub-)linear reaction. Using variational methods combined with Morse theory, we prove two multiplicity theorems providing precise sign information for all the solutions (constant sign and nodal solutions). In the process, we prove two auxiliary results of independent interest.

(p,2)

Existence and uniqueness of solutions to a second order nonlinear nonlocal hyperbolic equation fully nonlinear programming problems with closed range operators internal stabilization of the diffusion equation flow-invariant sets with respect to Navier-Stokes equation numerical approximation of the Ricatti equation via fractional steps method asymptotic analysis of the telegraph system with nonlinear boundary conditions global existence for a class of dispersive equations viable domains for differential equations governed by caratheodory perturbations of nonlinear m-accretive operators almost periodic solutions to neural functional equations the one-dimensional wave equation with Wentzell boundary conditions on the longterm behaviour of a parabolic phase-field model with memory on the Kato classes of distributions and BMO-classes the global solution set for a class of semilinear problems optimal control and algebraic Ricatti equations under singular estimates for eAtB in the absence of analyticity the stable case solving identification problems for the wave equation by optimal control methods singular perturbations and approximations for integrodifferential equations remarks on impulse control problems for the stochastic Navier-Stokes equations recent progress on the Lavrentiev phenomenon, with applications abstract eigenvalue problem for monotone operators and applications to differential operators implied volatility for American options via optimal control and fast numerical solutions of obstacle problems first order necessary conditions of optimality for semilinear optimal control problems Lyapunov equation and the stability of nonautonomous evolution equations in Hilbert spaces least action for N-body problems with quasihomogeneous potentials.

-equations

We consider a nonlinear Neumann problem, driven by the