We study the Dirichlet boundary value problem for the p-Laplacian of the form −∆pu − λ1|u| p−2u = f in Ω, u = 0 on ∂Ω, where Ω ⊂ N is a bounded domain with smooth boundary ∂Ω, N ≥ 1, p > 1, f ∈ C(Ω) and λ1 > 0 is the first eigenvalue of ∆p. We study the geometry of the energy functional Ep(u) = 1⁄ p ∫ Ω |∇u| p − λ1⁄ p ∫ Ω |u| p − ∫ Ω fu and show the difference between the case 1 <p< 2 and the case p > 2. We also give the characterization of the right hand sides f for which the above Dirichlet problem is solvable and has multiple solutions.
DPC played an important role in regulating the production, translocation and partítioning of i‘*C-assimilates in cotton {Gossypium hirsutum L.) plants. Seed soaking with DPC increased the partítioning of cotton assimilates into roots aitd main stem, and decreased the partítioning into seedling tip which was beneficial for the seedling. After the appearance of a square, spraying with DPC decreased the partítioning of assimilates into the main stem, branches and their growing points, and increased the partítioning into reproductíve organs and roots. This helped to avoid or reduce spindling, ensured a steady growth, coordination of the relatíon between vegetatíve and reproductíve organs, and improved the development of floral buds. From bloom to boll-setting,. sprayings with DPC greatly increased the partítioning of assimilates into reproductíve organs and decreased the partítioning into vegetatíve organs, which was usefiil for the growth and development of squares and bolls.