Abstract Let $(M,g)$ ( M , g ) be an n -dimensional complete Riemannian manifold with nonnegative Ricci curvature. In this paper, we consider overdetermined problem of the biharmonic operator on a bounded smooth domain Ω in M . We deduce that...

In this chapter a meshless method, based on the method of fundamental solutions (MFS) and radial basis functions (RBF), is developed to solve thin plate bending on an elastic foundation. In the presented algorithm, the analog equation method (AEM) is firstly used to convert the original governing equation to an equivalent thin plate bending equation without elastic foundations, which can be sol...

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 shows the existence of at least three solutions for Navier problem involving the p(x)-biharmonic operator. Our technical approach is based on a theorem obtained by B. Ricceri.