BLOWING UP AND MULTIPLICITY OF SOLUTIONS FOR A FOURTH-ORDER EQUATION WITH CRITICAL NONLINEARITY

作     者：Siwar AMMAR Mokhles HAMMAMI 

作者机构：Department of mathematics University of Monastir Department of mathematics Faculty of Sciences of sfax University of Sfax 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2015年第35卷第6期

页      面：1511-1546页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0704[理学-天文学] 0701[理学-数学] 

主　　题：fourth order elliptic equations critical Sobolev exponent blow up solution 

摘      要：In this paper, we consider the following nonlinear elliptic problem ： △2u =｜u｜n-4^-u＋u｜u｜q-1u,in Ω,△u=u=0 on ЭΩ,where Ω is a bounded and smooth domain in R^n,n∈{5,6,7},u is a parameter and q∈]4/（n-4）,（12-n）/（n-4）].We study the solutions which concentrate around two points of Ω. We prove that the concentration speeOs are the same order and the distances of the concentration points from each other and from the boundary are bounded. For Ω=（Ωa）a a smooth ringshaped open set, we establish the existence of positive solutions which concentrate at two points of Ω. Finally, we show that for u〉0, large enough, the problem has at least many positive solutions as the Ljusternik-Schnirelman category of Ω.