On a comparison theorem for strongly elliptic systems

Existence Results for Strongly Indefinite Elliptic Systems

In this paper, we show the existence of solutions for the strongly indefinite elliptic system −∆u = λu+ f(x, v) in Ω, −∆v = λv + g(x, u) in Ω, u = v = 0, on ∂Ω, where Ω is a bounded domain in RN (N ≥ 3) with smooth boundary, λk0 < λ < λk0+1, where λk is the kth eigenvalue of −∆ in Ω with zero Dirichlet boundary condition. Both cases when f, g being superlinear and asymptotically linear at infin...

Designing a hybrid quantum controller for strongly eigenstate controllable systems

 In this paper, a new quantum hybrid controller for controlling the strongly eigenstate controllable systems, is designed. For this purpose, a Lyapunov control law is implemented when the target state is in reachable set of the initial state. On the other hand, if the target state is not in the reachable set of the given initial state, based on Grover algorithm, a new interface state that the t...

Proof of a Recurrence Theorem for Strongly Transitive Systems.

Strongly Elliptic Systems and Boundary Integral Equations

Partial differential equations provide mathematical models of many important problems in the physical sciences and engineering. This book treats one class of such equations, concentrating on methods involving the use of surface potentials. It provides the first detailed exposition of the mathematical theory of boundary integral equations of the first kind on non-smooth domains. Included are cha...

On a Comparison Theorem for Self-adjoint Partial Differential Equations of Elliptic Type