Multiplicity of Solutions to the Quasilinear Neumann Problem in the 3-Dimensional Case

Multiplicity of positive solutions for a critical quasilinear Neumann problem

“…Since by assumption µ(B) = lim λ→∞ I λ [u λ ] ≤ K(n, p)m(A) 1− p q we conclude that α = 1. Recalling that for u ∈ X u Lq(S) = 1 we get (8).…”

“…Suppose that there is a δ-function outside of A. From (8) follows that for large λ almost all of ν(S) mass is concentrated in a κ-neighbourhood of A, and according to (11) there are no δ-functions outside of that neighbourhood.…”

“…The problems (1) and (2) were studied later by many authors for subcritical q (see e.g. [17,8,10,11,4]). In [20] the multiplicity result was obtained for the Neumann problem…”

A survey of results of St.Petersburg State University research school on nonlinear partial differential equations I

“…Назаров [127] получил аналогичные результаты для уравнения с оператором p-лапласиана (4) в левой части уравнения (14). Для ряда других краевых задач эффект множественности был исследован им и его учениками [128][129][130][131][132][133][134][135]. Вариационный метод построения решений с различными симметриями для квазилинейных уравнений во всем пространстве был предложен в [136].…”