MULTIPLICITY OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR GENERALIZED HENON EQUATION

摘要

For the boundary value problem —Δ_pu = |x|~αu~(q-1) in B_1, u|_(partial deriv B_1) =0 and some more general problems the existence of any a priori given number of different positive solutions is established under suitable conditions on q and a. Nonradial solutions to the problem are constructed for some supercritical q. Bibliography. 30 titles.