The biharmonic supercritical equation ∆u = |u|p−1u, where n > 4 and p > (n + 4)/(n − 4), is studied in the whole space R as well as in a modified form with λ(1 + u) as right-hand-side with an additional eigenvalue parameter λ > 0 in the unit ball, in the latter case together with Dirichlet boundary conditions. As for entire regular radial solutions we prove oscillatory behaviour around the expl...

This paper studies some properties of F-biharmonic maps between Riemannian manifolds. By considering the first variation formula of the F-bienergy functional, F-biharmonicity of conformal maps are investigated. Moreover, the second variation formula for F-biharmonic maps is obtained. As an application, instability and nonexistence theorems for F-biharmonic maps are given.

This report investigates the paper Lipman et al. Biharmonic distance, who introduced a new distance measure, called biharmonic. We examine the approach of the distance, which is based on the Green’s kernel of the Bi-Laplacian in the continuous and the discrete setting. For the discrete setting we have two different methods of calculation, an approximate as well as an exact computation. Furtherm...

We classify the space-like biharmonic surfaces in 3dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.

background: pentoxifylline (px) is a methyxanthin derivative that influences the sperm motion characteristics. in general, px has been reportedly effective in preserving sperm motility in vitro, also when administered orally to the asthenozoospermic patients. objective: the main objective of this prospective clinical trial study was to rule out the effect of oral administration of px on sperm p...

in this paper, biharmonic slant helices are studied according to bishop frame in the heisenberg group heis3. we give necessary and sufficient conditions for slant helices to be biharmonic. the biharmonic slant helices arecharacterized in terms of bishop frame in the heisenberg group heis3. we give some characterizations for tangent bishop spherical images of b-slant helix. additionally, we illu...

Biharmonic surfaces in Euclidean space $mathbb{E}^3$ are firstly studied from a differential geometric point of view by Bang-Yen Chen, who showed that the only biharmonic surfaces are minimal ones. A surface $x : M^2rightarrowmathbb{E}^{3}$ is called biharmonic if $Delta^2x=0$, where $Delta$ is the Laplace operator of $M^2$. We study the $L_k$-biharmonic spacelike hypersurfaces in the $4$-dimen...

In this paper, the reduction of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map of an arbitrary compact Riemannian manifold into a compact Lie group (G, h) with bi-invariant Riemannian metric h is obtained. By this formula, all biharmonic curves into compaqct Lie groups are determined, and all the biharmonic maps of an open domain of R with the conformal metric of ...