In this paper, we extend the definition of p-harmonic and p-biharmonic maps between Riemannian manifolds. We present some new properties for generalized stable maps.

In this paper, we deal with the biharmonic heat equation gradient non-linearity. Under suitable condition of initial datum, show that global unique existence mild solution. The main technique in paper is to use Banach?s fixed point theorem combination Lp-Lq evaluation operator.

We clarify the validity of a method that decouples a boundary value problem of biharmonic equation to two Poisson equations on polygonal domains. The method provides a way of computing deflections of simply supported polygonal plates by using Poisson solvers. We show that such decoupling is not valid if the polygonal domain is not convex. It may fail even when the right hand side function is in...

In this article, a new biorthogonal multiwavelet basis on the interval with complementary homogeneous Dirichlet boundary conditions of second order is presented. This construction is based on the multiresolution analysis onR introduced in [DHJK00] which consists of cubic Hermite splines on the primal side. Numerical results are given for the Riesz constants and both a non-adaptive and an adapti...

In this work we study the existence of solutions for the nonlinear eigenvalue problem with p-biharmonic ∆pu = λm(x)|u|p−2u in a smooth bounded domain under Neumann boundary conditions.

Recommended by Narendra Kumar Govil We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions their boundaries are determined explicitly and the proofs rely on Schw...

<p style='text-indent:20px;'>In this paper, we consider the weighted fourth order equation</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \Delta(|x|^{-\alpha}\Delta u)+\lambda \text{div}(|x|^{-\alpha-2}\nabla u)+\mu|x|^{-\alpha-4}u = |x|^\beta u^p\quad \text{in} \quad \mathbb{R}^n \backslash \{0\}, $\end{document...

In this paper, non-geodesic biharmonic curves in ̃ SL(2, R) space are characterized and the statement that only proper biharmonic curves are helices is proved. Also, the explicit parametric equations of proper biharmonic helices are obtained. AMS subject classifications: 53A40