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.
|Number of pages||25|
|Journal||Calculus of Variations and Partial Differential Equations|
|Publication status||Published - 1 Nov 2015|