Journal
APPLICABLE ANALYSIS
Volume 92, Issue 2, Pages 411-423Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00036811.2011.625013
Keywords
Dirichlet problem; positive solutions; critical points; 35J20; 35J60; 35J91
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The existence of non-trivial solutions for nonlinear Dirichlet problems involving the p-Laplacian is investigated. In particular, an existence result of at least one non-trivial solution, without requiring any asymptotic condition on the nonlinear term either at zero or at infinity, is presented. As a consequence, also a multiplicity result is pointed out. The approach is based on a local minimum theorem for differentiable functionals.
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