Multiplicity results for some fourth-order elliptic equations

SOME n - RECTANGLE NONCONFORMING ELEMENTS FOR FOURTH ORDER ELLIPTIC EQUATIONS

Motivated by both theoretical and practical interests, we will consider n-rectangle (n ≥ 2) nonconforming finite elements for n-dimensional fourth order partial equations in this paper. In the two dimensional case, there are well-known nonconforming elements, such as the Morley element, the Zienkiewicz element and the Adini element, etc (see [1-4]). In a recent paper [10], we have discussed the...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Multiplicity Results for Perturbed Fourth-order Kirchhoff-type Problems

Nonconforming tetrahedral finite elements for fourth order elliptic equations

This paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed elements include two nonconforming tetrahedral finite elements and one quasi-conforming tetrahedral element. These elements are proved to be convergent for a model biharmonic equation in three...

Concentration Phenomena for Fourth-order Elliptic Equations with Critical Exponent

We consider the nonlinear equation ∆u = u n+4 n−4 − εu with u > 0 in Ω and u = ∆u = 0 on ∂Ω. Where Ω is a smooth bounded domain in Rn, n ≥ 9, and ε is a small positive parameter. We study the existence of solutions which concentrate around one or two points of Ω. We show that this problem has no solutions that concentrate around a point of Ω as ε approaches 0. In contrast to this, we construct ...