In general, for higher order elliptic equations and boundary value problems like the biharmonic equation and the linear clamped plate boundary value problem neither a maximum principle nor a comparison principle or – equivalently – a positivity preserving property is available. The problem is rather involved since the clamped boundary conditions prevent the boundary value problem from being rea...

This paper deals with the existence of solutions a p-biharmonic pseudo parabolic partial differential equation logarithmic nonlinearity in bounded domain. We prove global weak using Faedo-Galerkin method and applying concavity approach, that blow up at finite time. Further, we provide maximal limit for blow-up

We consider the focusing inhomogeneous biharmonic nonlinear Schrödinger equation in $$H^2(\mathbb {R}^N)$$ , $$\begin{aligned} iu_t + \Delta ^2 u - |x|^{-b}|u|^{\alpha }u=0, \end{aligned}$$ when $$b > 0$$ and $$N \ge 5$$ . first obtain a small data global result $$H^2$$ which, five-dimensional case, improves previous from Pastor second author. In sequel, we show main result, scattering below ma...

Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove t...