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论文类型：期刊论文

发表时间：2012-01-01

发表刊物：APPLICABLE ANALYSIS

收录刊物：SCIE、Scopus

卷号：91

期号：11

页面范围：2045-2055

ISSN号：0003-6811

关键字：Kirchhoff type equation; mountain pass theorem; fountain theorem; variational methods

摘要：In this article, we study the existence and multiplicity results for Kirchhoff type equations of the form
   {-(a + b integral(Omega) |del u|(2) dx)Delta u = f(x, u), in Omega, (*)
   u = 0, on partial derivative Omega,
   where f is an element of C((Omega) over bar x R, R) is three-superlinear at infinity. Under certain assumptions on f, we obtain at least one nontrivial solution for (*) without assuming the Ambrosetti and Rabinowitz condition by using the mountain pass theorem, and obtain infinitely many solutions when f(x, .) is odd by using the fountain theorem.