We prove some Liouville type results for stable solutions to the biharmonic problem ∆u = u, u > 0 in R where 1 < q < ∞. For example, for n ≥ 5, we show that there are no stable classical solution in R when n+4 n−4 < q ≤ ( n−8 n )−1 + .

Contrary to the second order case, biharmonic heat kernels are sign-changing. A deep knowledge of their behaviour may however allow to prove positivity results for solutions of the Cauchy problem. We establish further properties of these kernels, we prove some Lorch-Szegö-type monotonicity results and we give some hints on how to obtain similar results for higher polyharmonic parabolic problems.

For a semilinear biharmonic Dirichlet problem in the ball with supercritical power-type nonlinearity, we study existence/nonexistence, regularity and stability of radial positive minimal solutions. Moreover, qualitative properties, and in particular the precise asymptotic behaviour near x = 0 for (possibly existing) singular radial solutions, are deduced. Dynamical systems arguments and a suita...

In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the doubly warped product f B ×b F can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections f B ×b F → B and f B ×b F → F , respectively. Some characterizations for non-harmonic biharmonic maps are g...

Jacobsen syndrome (JBS) is a rare congenital disorder caused by a terminal deletion of the long arm of chromosome 11. A subset of patients exhibit social behavioural problems that meet the diagnostic criteria for autism spectrum disorder (ASD); however, the underlying molecular pathogenesis remains poorly understood. PX-RICS is located in the chromosomal region commonly deleted in JBS patients ...

Directed-ratchet transport (DRT) in a one-dimensional lattice of spherical beads, which serves as a prototype for granular chains, is investigated. We consider a system where the trajectory of the central bead is prescribed by a biharmonic forcing function with broken time-reversal symmetry. By comparing the mean integrated force of beads equidistant from the forcing bead, two distinct types of...

We construct infinitely many real-valued, time-periodic breather solutions of power-type nonlinear wave equations. These are obtained from critical points a dual functional and they weakly localized in space. Our abstract framework allows to find similar existence results for the Klein-Gordon equation or biharmonic

Iterative methods to achieve a suitable linearization as well as a decrease of the order and dimension of nonlinear partial differential equations of the eighth order into the biharmonic and Poisson-type differential equations with their simultaneous linearization are proposed in this work. Validity and reliability of the obtained results are discussed using computer programs developed by the a...

We propose an eecient implementation of the Chebyshev Galerkin spectral method for the biharmonic operator. This discretization leads to banded matrices which, compared with other methods of the same type, are also better conditioned. The eeciency of the method is illustrated on the Orr-Sommerfeld eigenvalue problem, where an improved convergence can be observed and the spurious eigenvalues are...

A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For corresponding equation involution, we investigated solvability boundary value problems a fractional-order having derivative Hadamard-type. First, involution type were The properties matrices these investigated. As applications considered transformations, questions about problem for studied. M...