Journal
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume 4, Issue 1, Pages 9-22Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2005.4.9
Keywords
p&q-Laplacian; variational principles; existence of non-negative solution
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In this paper, we analyse a family of stationary nonlinear equations with p&q- Laplacian -Delta(p)u - Delta(q)u = lambda c(x, u) which have a wide spectrum of applications in many areas of science. We introduce a new type of variational principles corresponding to this family of equations. Using this formalism, we exhibit intervals for the scalar parameter lambda where there exist positive solutions of the considered problems. Furthermore, we prove, in another interval, the nonexistence of nontrivial solutions. These results are different from those of existence and nonexistence for stationary equations with single Laplacian.
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