Given a prescribed boundary of a Bézier surface, we compare the Bézier surfaces generated by two different methods, i.e., the Bézier surface minimising the biharmonic functional and the unique Bézier surface solution of the biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper, we prov...

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

We are interested in entire solutions for the semilinear biharmonic equation ∆u = f(u) in R , where f(u) = e or −u−p (p > 0). For the exponential case, we prove that for the polyharmonic problem ∆u = e with positive integer m, any classical entire solution verifies ∆2m−1u < 0, this completes the results in [6, 14]; we obtain also a refined asymptotic expansion of radial separatrix solution to ∆...

The paper studies boundary integral operators of the bi{Laplacian on piecewise smooth curves with corners and describes their mapping properties in the trace spaces of variational solutions of the biharmonic equation. We formulate a direct integral equation method for solving mixed boundary value problems for the biharmonic equation on a nonsmooth plane domain, analyse the solvability of the co...

The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$-biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.

The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk D in C arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of t...

This paper is concerned with the study of the existence of positive solutions for a Navier boundaryvalue problem involving the p-biharmonic operator; the right hand side of problem is a nonsmoothfunctional with variable parameters. The existence of at least three positive solutions is establishedby using nonsmooth version of a three critical points theorem for discontinuous functions. Our resul...

‎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 ‎$h_1(x)‎, ‎h_2(x)$‎.