| 一类非线性4阶椭圆方程解的多重性 |
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| 引用本文： | 郑旭东,燕艳菊,吕志伟,张延凤.一类非线性4阶椭圆方程解的多重性[J].河南师范大学学报(自然科学版),2014(1):31-35. |
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| 作者姓名： | 郑旭东 燕艳菊 吕志伟 张延凤 |
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| 作者单位： | ;1.安阳工学院数理学院;2.大连东软集团 |
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| 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
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| 关 键 词： | 特征值 山路引理 变分环绕定理 |
Multiple Nontrivial Solutions for a Fourth-Order Nonlinear Elliptic Equation |
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| Institution: | ,Department of Mathematics and Physics,Anyang Institute of Technology,Neusoft |
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| Abstract: | 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 Gsatisfies the P.S.condition is proved.with the mountain pass theorem and the variation of linking theorem,we discuss that if b1-b2 <Λ1(c)and b2 <0,the equation has at least two solutions.And if b2 >0,b1 <Λ3(c),0Λ2(c),the equation has at least three solutions. |
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| Keywords: | eigenvalue mountain pass theorem linking theorem |
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