Existence and multiplicity of positive solutions for the fourth order equation u′′′′ − M( ∫ 1 0 |u ′|2 dx)u′′ = q(x)f(x, u, u′), which models simply supported extensible beams, are considered using fixed point theorems in cones of ordered Banach spaces.

In this paper, we consider the Robin-Dirichlet problem for a nonlinear wave equation of Kirchhoff-Carrier type with Balakrishnan-Taylor damping. First, under suitable conditions on initial data, local existence and uniqueness weak solution are proved. Next, an asymptotic expansion solutions in small parameter high order is established. The used main tools linearization method terms together Fae...

motivated by the problem of vertical flexion of fully clamped beams. Our main goal in this paper is to study the properties previously mentioned when the set D is a time-dependent nonempty bounded subset Ωt of Rn, which means that the supports of the extremes of the beam have small displacements. Note that the sets Ωt , where u=u(x,t) is defined, change with the time, which yields a noncylindri...

Questions on the existence of positive solutions for the following class of elliptic problems are studied: − M ‖u‖p1,p 1,p Δpu f x, u , in Ω, u 0, on ∂Ω, where Ω ⊂ R is a bounded smooth domain, f : Ω ×R → R and M : R → R, R 0,∞ are given functions. Copyright q 2008 F. J. S. A. Corrêa and R. G. Nascimento. This is an open access article distributed under the Creative Commons Attribution License,...

and Applied Analysis 3 for pole point selection. After that, we iteratively solve the Kirchhoff equation to perform clustering. Finally, we get the clustering result. In this paper, we consider only the 2community clustering case and will leave the case of k cluster problem into the future research.