Release Time:2019-03-13  Hits:

Indexed by: Journal Article

Date of Publication: 2018-01-01

Journal: INDIANA UNIVERSITY MATHEMATICS JOURNAL

Included Journals: SCIE

Volume: 67

Issue: 6

Page Number: 2103-2121

ISSN: 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].