We consider the operator − d 2 dr2 −V in L2(R+) with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound tr „

We consider the asymptotic analysis and some existence result on blowing up solutions for a semilinear elliptic equation in dimension 2 with nonlinear exponential term, singular sources and Dirichlet boundary condition.

In this paper, we investigate a nonlocal semilinear heat equation with homogeneous Dirichlet boundary condition in a bounded domain, and prove that there exist solutions with positive initial energy that blow up in finite time.

Let Ω be a bounded subset of Rn with smooth boundary. We investigate the solvability for a class of the system of the nonlinear elliptic equations with Dirichlet boundary condition. Using the mountain pass theorem we prove that the system has at least one nontrivial solution.

We give a necessary and sufficient condition, of geometrical type, for the uniform decay energy solutions linear system magnetoelasticity in bounded domain with smooth boundary. A Dirichlet-type boundary condition is assumed. Our strategy to use microlocal defect measures show suitable observability inequalities on high-frequency Lamé system.

in this paper, two inverse problems of stephen kind with local (dirichlet) boundary conditions are investigated. in the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. for the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

(1)  ut −∆u = f in Ω× (0, T ), u = 0 on ∂Ω× (0, T ), u(·, 0) = u0 in Ω. Here u = u(x, t) is a function of spatial variable x ∈ Ω and time variable t ∈ (0, T ). The Laplace differential operator ∆ is taking with respect to the spatial variable. For the simplicity of exposition, we consider only homogenous Dirichlet boundary condition and comment on the adaptation to Neumann and other type of b...

We study the stability of solutions to a coupled evolution system associated with an isotropic porous and centrosymmetric viscoelastic solid with porous dissipation (a porous elastic system with history). With the help of the method of the semigroup theory and some novel observations, we prove successfully that the condition of equal wave-speed propagation is still necessary for exponential sta...

In this article, we investigate the exact controllability of the 2DSchrödinger-Poisson system, which couples a Schrödinger equation on a bounded domain of R with a Poisson equation for the electrical potential. The control acts on the system through a Neumann boundary condition on the potential, locally distributed on the boundary of the space domain. We prove several results, with or without n...