Release Time:2019-03-09  Hits:

Indexed by: Journal Article

Date of Publication: 2012-01-01

Journal: APPLICABLE ANALYSIS

Included Journals: Scopus、SCIE

Volume: 91

Issue: 11

Page Number: 2045-2055

ISSN: 0003-6811

Key Words: Kirchhoff type equation; mountain pass theorem; fountain theorem; variational methods

Abstract: 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.