On positive solutions for (p, q)-Laplace equations with two parameters

Vladimir Bobkov, Mieko Tanaka

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We study the existence and non-existence of positive solutions for the (p, q)-Laplace equation (Formula Presented.), where p≠q, under the zero Dirichlet boundary condition in Ω. The main result of our research is the construction of a continuous curve in (α,β) plane, which becomes a threshold between the existence and non-existence of positive solutions. Furthermore, we provide the example of domains Ω for which the corresponding first Dirichlet eigenvalue of -Δp is not monotone w.r.t. p>1.

Original languageEnglish
Pages (from-to)3277-3301
Number of pages25
JournalCalculus of Variations and Partial Differential Equations
Issue number3
Publication statusPublished - 1 Nov 2015



  • 35J20
  • 35J62
  • 35P30

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