Biharmonic eigen-value problems andLpestimates

Bounds on the First Nonzero Eigen- Value for Self-adjoint Boundary Value Problems on Networks

We aim here at obtaining bounds on the first nonzero eigenvalue for selfadjoint boundary value problems on a weighted network by means of equilibrium measures, that include the study of Dirichlet, Neumann and Mixed problems. We also show the sharpness of these bounds throughout the analysis of some examples. In particular we emphasize the case of distance-regular graphs and we show that the obt...

Sinc Solution of Biharmonic Problems

In this paper we solve two biharmonic problems over a square, B = (−1, 1) × (−1, 1). (1) The problem ∇4U = f , for which we determine a particular solution, U , given f , via use of Sinc convolution; and (2) The boundary value problem ∇4V = 0 for which we determine V given V = g and normal derivative Vn = h on ∂B, the boundary of B. The solution to this problem is carried out based on the identity

A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

This paper reports a new spectral collocation method for numerically solving two-dimensional biharmonic boundary-value problems. The construction of the Chebyshev approximations is based on integration rather than conventional differentiation. This use of integration allows: (i) the imposition of the governing equation at the whole set of grid points including the boundary points and (ii) the s...

Boundary Value Problems for Singular Ordinary Differential Equations. A Widely Applicable Method for Calculating Eigen-Values

On a class of boundary value problems involving the p-biharmonic operator

A nonlinear boundary value problem involving the p-biharmonic operator is investigated, where p > 1. It describes various problems in the theory of elasticity, e.g. the shape of an elastic beam where the bending moment depends on the curvature as a power function with exponent p− 1. We prove existence of solutions satisfying a quite general boundary condition that incorporates many particular b...