In this paper, we establish the existence of at least three solutions to a Navier boundary problem involving the biharmonic equation. The technical approach is mainly base on a three critical points theorem of B. Ricceri. AMS Subject Classifications: 34B15.

We study the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. We analyze the problem via an implicit time discretization, and we prove some regularity properties of the solution.

We consider a two obstacle problem for the parabolic biharmonic equation in a bounded domain. We prove long time existence of solutions via an implicit time discretization scheme, and we investigate the regularity properties of solutions.

The purpose of this paper is to establish the regularity the weak solutions for the nonlinear biharmonic equation { ∆2u + a(x)u = g(x, u), u ∈ H2(RN ), where the condition u ∈ H2(RN ) plays the role of a boundary value condition, and as well expresses explicitly that the differential equation is to be satisfied in the weak sense.

In this note we use the Nehari manifold and fibering maps to show existence of positive solutions for a nonlinear biharmonic equation in a bounded smooth domain in Rn, when n = 5, 6, 7. Mathematics Subject Classification: 35J35, 35J40

‎using variational arguments‎, ‎we prove the existence of infinitely‎ ‎many solutions to a class of $p$-biharmonic equation in‎ ‎$mathbb{r}^n$‎. ‎the existence of‎ ‎nontrivial‎ ‎solution is established under a new‎ ‎set of hypotheses on the potential $v(x)$ and the weight functions‎ ‎$h_1(x)‎, ‎h_2(x)$‎.

In this work, we use a symbolic algebra package to derive a family of nite diierence approximations for the biharmonic equation on a 9 point compact stencil. The solution and its rst derivatives are carried as unknowns at the grid points. Dirichlet boundary conditions are thus incorporatednaturally. Since the approximations use the 9 point compact stencil, no special formulas are needed near th...

A mixed formulation with two main variables, based on the Ciarlet-Raviart technique, with 0 C continuity shape functions is employed for the solution of some types of biharmonic equations in 1-D. The continuous and discrete Babuška-Brezzi inf-sup conditions are established. The formulation is numerically tested for both the hand pextensions. The model problems involve the standard biharmonic eq...

Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation tha...

In this work, we compare different mesh moving techniques for monolithically-coupled fluid-structure interactions in arbitrary Lagrangian–Eulerian coordinates. The mesh movement is realized by solving an additional partial differential equation of harmonic, linear-elastic, or biharmonic type. We examine an implementation of time discretization that is designed with finite differences. Spatial d...