一类非线性4阶椭圆方程解的多重性  

Multiple Nontrivial Solutions for a Fourth-Order Nonlinear Elliptic Equation

作　　者：郑旭东[1] 燕艳菊[1] 吕志伟[1] 张延凤[2] 

机构地区：[1]安阳工学院数理学院,河南安阳455000 [2]大连东软集团,辽宁大连116023

出　　处：《河南师范大学学报（自然科学版）》2014年第1期31-35,共5页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11271336);河南省青年骨干教师基金(2011GGJS-213)

摘　　要：主要考察了满足狄利克莱边界条件的一类非线性4阶椭圆方程.首先定义了方程的相伴泛函G,证明了G满足P.S.条件.其次,利用山路引理和变分环绕定理,讨论了当b1-b2<Λ1(c),b2<0时,方程至少有2个解;当b1-b2>Λ2(c),b2>0,0<b1<1T及b1<Λ3(c)时,方程至少有3个解.In this paper, a nonlinear fourth-order elliptic equation under the Dirichlet boundary condition is investigated. The associated functional Gcorresponding to the equation is defined and that the functional G satisfies the P. S. condition is proved, with the mountain pass theorem and the variation of linking theorem, we discuss that if bl --bz 〈A1 （c） and b2 〈0, the equation has at least two solutions. And if b2 〉0,bl 〈A3 （c）,0〈bl 〈1 and b1 --b2 〉A2 （c）, the equation has at least three solutions.

关 键 词：特征值 山路引理 变分环绕定理 

分 类 号：O175.25[理学—数学]