The three-nucleon ground state and the N–d scattering states are obtained using variational principles. The wave function of the system is decomposed into angular–spin–isospin channels and the corresponding two dimensional spatial amplitudes are expanded in a correlated polynomial basis. For the scattering states, the complex form of the Kohn variational principle is used to determine the S–mat...

We consider the classical autonomous constrained variational problem of minimization of ∫ b a f(v(t), v ′(t))dt in the class Ω:={v ∈ W 1,1(a, b) : v(a) = α, v(b) = β, v′(t) ≥ 0 a.e. in (a, b)}, where f : [α, β] × [0,+∞) → R is a lower semicontinuous, nonnegative integrand, which can be nonsmooth, nonconvex and noncoercive. We prove a necessary and sufficient condition for the optimality of a tr...

A new system of generalized mixed quasivariational inclusions for short, SGMQVI with relaxed cocoercive operators, which develop some preexisting variational inequalities, is introduced and investigated in Banach spaces. Next, the existence and uniqueness of solutions to the problem SGMQVI are established in real Banach spaces. From fixed point perspective, we propose some new iterative algorit...

Sensitivity analysis of solution for variational inequalities and variational inclusions has been studied by many authors via quite different technique. See 1–7 and the reference therein . In 2004, Agarwal et al. 1 introduced and studied the following problem which is called the system of parametric generalized nonlinear mixed quasi variational inclusions. Let H be a real Hilbert space endowed ...

The paper considers nonsmooth neural networks described by a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs include the relevant class of neural networks, introduced by Li, Michel and Porod, described by linear systems evolving in a closed hypercube of R(n). The main result in the paper is a necessary and sufficient condition for multistability of...

This paper studies optimal control problems for dynamical systems governed by neutral functional-differential inclusions that linearly depend on delayed velocity variables. Developing the method of discrete approximations, we derive new necessary optimality conditions for such problems in both EulerLagrange and Hamiltonian forms. The results obtained are expressed in terms of advanced generaliz...

An important advantage of variational data assimilation methods is that observations that differ from the analysis variables can be directly analyzed as long as they can be expressed in terms of the model state variables. Examples include radar radial velocity and reflectivity, the GPS precipitable water, and satellite radiances. A variational method produces an analysis that minimizes a cost f...