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论文类型：期刊论文

发表时间：2015-09-01

发表刊物：TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS

收录刊物：SCIE、Scopus

卷号：46

期号：1

页面范围：135-163

ISSN号：1230-3429

关键字：Eigenvalue; bifurcation; convex solution; Monge-Ampere equation

摘要：In this paper we study the following eigenvalue boundary value problem for Monge-Ampere equations
   {det(D(2)u) = lambda(N) f(-u) in Omega,
   u = 0 on partial derivative Omega.
   We establish global bifurcation results for the problem with f(u) = u(N) + g(u) and Omega being the unit ball of R-N. More precisely, under some natural hypotheses on the perturbation function g: [0, +infinity) -> [0, +infinity), we show that (lambda(1), 0) is a bifurcation point of the problem and there exists an unbounded continuum of convex solutions, where lambda(1) is the first eigenvalue of the problem with f(u) = u(N). As the applications of the above results, we consider with determining interval of lambda, in which there exist convex solutions for this problem in unit ball. Moreover, we also get some results about the existence and nonexistence of convex solutions for this problem on general domain by domain comparison method.