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Indexed by:期刊论文

Date of Publication:2018-01-01

Journal:INDIANA UNIVERSITY MATHEMATICS JOURNAL

Included Journals:SCIE

Volume:67

Issue:6

Page Number:2103-2121

ISSN No.:0022-2518

Key Words:Bifurcation; mean curvature operator; topological method

Abstract:We establish the existence/nonexistence and multiplicity of nontrivial nonnegative solutions for the following 0-Dirichlet problem with mean curvature operator in the Minkowski space
   {-div(del u/root 1-|del u|(2)) = lambda f(x,u) in Omega,
   u = 0 on partial derivative Omega,
   where Omega is a general bounded domain of R-N. By bifurcation and topological methods, we determine the interval of parameter lambda in which the above problem has zero/one/two nontrivial nonnegative solutions according to sublinear/linear/superlinear nonlinearity at zero. Moreover, we also amend a minor fault in [2, Proposition 1.1].