We consider the nonlinear biharmonic Schr\"odinger equation $$i\partial_tu+(\Delta^2+\mu\Delta)u+f(u)=0,\qquad (\text{BNLS})$$ in critical Sobolev space $H^s(\R^N)$, where $N\ge1$, $\mu=0$ or $-1$, $0<s<\min\{\fc N2,8\}$ and $f(u)$ is a function that behaves like $\lambda\left|u\right|^{\alpha}u$ with $\lambda\in\mathbb{C},\alpha=\frac{8}{N-2s}$. prove existence uniqueness of global solutions t...

This paper is concerned with an inverse source problem for the stochastic biharmonic wave equation. The driven assumed to be a microlocally isotropic Gaussian random field its covariance operator being classical pseudo-differential operator. well-posedness of direct examined in distribution sense, and regularity solution discussed given rough source. For problem, strength source, involved princ...

Let Ω be a bounded Lipschitz domain in Rn, n ≥ 3. Let L be a second order elliptic system with constant coefficients satisfying the Legendre-Hadamard condition. We consider the Dirichlet problem Lu = 0 in Ω, u = f on ∂Ω with boundary data f in the Morrey space L2,λ(∂Ω). Assume that 0 ≤ λ < 2 + ε for n ≥ 4 where ε > 0 depends on Ω, and 0 ≤ λ ≤ 2 for n = 3. We obtain existence and uniqueness resu...