A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements u. The model is based on the biharmonic equation ∇u = 0 in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson grow...

the aim of this article is to establish the existence of at least three‎ ‎solutions for a perturbed $p$-biharmonic equation depending on two‎ ‎real parameters‎. ‎the approach is based on variational methods‎.

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.

In this article, we show the existence of at least three solutions to a Navier boundary problem involving the p(x)-biharmonic operator. The technical approach is mainly base on a three critical points theorem by Ricceri.

Abstract In this paper we study the biharmonic equation with Navier boundary conditions in a polygonal domain. particular, propose method that effectively decouples fourth-order problem as system of Poisson equations. Our differs from naive mixed leads to two problems but only applies convex domains; our decomposition involves third confine solution correct function space, and therefore can be ...

In this paper, we investigate the existence of infinitely many solutions for a class of biharmonic equations where the nonlinearity involves a combination of superlinear and asymptotically linear terms. The solutions are obtained from a variant version of Fountain Theorem.