Abstract: This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approxi...

In this article, we study the semilinear elliptic equation −∆u = |u|p(x)−2u, x ∈ R u ∈ D(R ), where N ≥ 3, p(x) = ( p, x ∈ Ω 2∗, x 6∈ Ω, with 2 < p < 2∗ := 2N/(N − 2), Ω ⊂ RN is a bounded set with nonempty interior. By using the Nehari manifold, we obtain a positive ground state solution.

This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations (sfdes) and fully nonlinear sfdes with a sublinear drift term. For the semilinear case, we use Malliavin ...

For any subcritical index of regularity s > 3/2, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space Hs × Hs−1 with certain angular regularity. The main new ingredient in the proof is an endpoint version of the generalized Strichartz estimates in the space Lt...

In this paper, we apply a successful combination of three key tools which allows to get a measure of the cost of the approximate controllability for semilinear heat equation. The first tool consists to get enough information about the approximate control for the linear heat equation with a potential depending on space-time variable. Then a fixed point method is applied. The fixed point techniqu...

4. Stable fuzzy control of multi-input and multi-output (mimo) perturbed linear systems 9. Existence and uniqueness of fuzzy solution for semilinear fuzzy integrodifferential equations with nonlocal conditions (2004), P. Balasubramaniam

In this paper, we investigate the languages generated by asynchronous spiking neural P systems. Characterizations of finite languages and recursively enumerable languages are obtained by asynchronous spiking neural P systems with extended rules. The relationships of the languages generated by asynchronous spiking neural P systems with regular and non-semilinear languages are also investigated. ...

We consider the semilinear elliptic problem −Δu + u = λK(x)up + f (x) in Ω, u > 0 in Ω, u ∈ H 0 (Ω), where λ ≥ 0, N ≥ 3, 1 < p < (N + 2)/(N − 2), and Ω is an exterior strip domain in RN . Under some suitable conditions on K(x) and f (x), we show that there exists a positive constant λ∗ such that the above semilinear elliptic problem has at least two solutions if λ∈ (0,λ∗), a unique positive sol...

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the control may change. Firstand secondorder optimality conditions are derived. The analysis is based on a reformulation involving a judiciously chosen transformation ...